What's (really) the difference between fruit and vegetables?

There is no real black and white definition of that difference, because where the line is drawn varies from crowd to crowd.

Botanically speaking, a fruit is a seed-bearing structure that develops from the ovary of a flowering plant, whereas vegetables are all other plant parts, such as roots, leaves and stems. By those standards, seedy outgrowths such as apples, squash and, yes, tomatoes are all fruits, while roots such as beets, potatoes and turnips, leaves such as spinach, kale and lettuce, and stems such as celery and broccoli are all vegetables.

The outlook is quite different in culinary terms, however. A lot of foods that are (botanically speaking) fruits, but which are savory rather than sweet, are typically considered vegetables by chefs. This includes such botanical fruits as eggplants, bell peppers and tomatoes.

You can find the whole article HERE, including this nice graph that I think nicely illustrates things.

All of your observations are correct - both the distinguishing factors and the fact that there are foods whose belonging to a category is unclear.

The reason behind this has nothing to do with cooking and everything to do with human cognition. Humans organize the information in their world in categories, which together build "folk taxonomies". For some reason, the prevailing opinion is that the categories in folk taxonomies work like mathematical sets, while the empirical data shows that they do not.

In school, we are taught that categories have a definition, and things either fulfill the definition, or don't. The definition is a bit like a boundary - if you define category X as "all natural numbers below 10", you know which numbers fall inside X and which fall outside.

In reality, all categories we use in everyday life are structured around prototype members. There are elements which feel like they truly represent the category, and other elements are more or less similar to the prototypes. This builds a core of elements which clearly belong, and others on the fringes of a category which might or might not belong, depending on how you want to argue.

Now I don't know of any research identifying which are the prototype elements of the categories "fruit" and "vegetable", or which are the important qualities which have to be partially or fully filled to be considered for membership in one of both categories. Taste is the only one I have seen given by food historians, who say that fruit played the role of candy before we learned to refine sugar, so the category depended more than what it is good for (a sweet treat, ready-to-eat) than on what it contains. Thus many botanical fruits became culinary vegetables due to lack of sweetness, but practically no other plant part became a culinary fruit, as the other parts do not have enough sugar concentration. But I am sure that if cognitive scientists have looked into the matter, they will have uncovered more criteria and will have measured whether a pepper or a potato is more prototypical of being a vegetable.

Bottom line, it is all convention. You will never find a strict definition.

The wikipedia article distinguishes between botanical fruits and culinary fruits. (Interestingly, both German ("Obst" vs. "Frucht") and Spanish ("Fruta" vs. "Fruto") have distinct terms for these.)

To quote:

In culinary terminology, a fruit is usually any sweet-tasting plant part, especially a botanical fruit; a...); and a vegetable is any savory or less sweet plant product.

(Both the German as well as Spanish Wikipedia articles support this loose definition.)

And the vegetable article says:

The term vegetable is somewhat arbitrary, and largely defined through culinary and cultural tradition. It normally excludes other food derived from plants such as fruits, nuts and cereal grains, but includes seeds such as pulses. The original meaning of the word vegetable, still used in biology, was to describe all types of plant, as in the terms "vegetable kingdom" and "vegetable matter".

There's a bit of confusion here because there are two senses of the word "fruit": the botanical sense with a more precise definition (plant parts with seeds), and the common everyday culinary usage with no precise definition (mostly sweet plant things).

In a culinary sense, i.e. talking about food, among chefs or just in common speech, there is no strict definition of fruit, and no completely precise delineation between fruit and vegetables. Sweetness and how it's eaten play a big part in defining fruit, as you've noted, and culinary fruits are mostly botanical fruits that meet those criteria, but that doesn't form a perfect definition. See rumtscho's excellent answer for more on how categories like this are (and aren't) defined. Vegetables, then, are basically everything from plants besides the fruit, also excluding grains.

This is the sense of "fruit" you'll generally hear. If you ask someone to organize a grocery store produce section, to go to the store and buy some fruit, or to put fruit in each lunch bag, they'll tend to use this sense of fruit/vegetable. So apples, oranges, and bananas will be fruits, while spinach, peppers, cucumbers, and beets will be vegetables.

But other things are less clear. For example, if you cook green plantains (starchy, not sweet, can be used much like potatoes) and ask someone if they're a fruit or a vegetable, you're pretty likely to get a response along the lines of "well, they're like bananas, so they must be fruit, but they're not sweet." And you could hear differing opinions on whether fresh corn is a vegetable or a grain.

Then there's the botanical sense, i.e. talking about parts of plants. In that sense, there's a strict definition: fruit is the seed-bearing structure of the plant. Other parts of the plant then have their own names; you'd talk about stems and leaves and roots, not vegetables.

You'll hear this sense in botany, such as "the fruit of the maple tree are called samaras or whirlybirds". It's similarly used in gardening, as in "my zucchini and tomato plants are bearing plenty of fruit".

Note that while it makes plenty of sense to talk about fruit in this context, it doesn't really make a lot of sense to talk about fruit vs vegetable in this context. You're not going to look at a tomato plant and say "it has a lot of fruit, and the vegetable parts look healthy too." You might talk about your garden as having fruit and vegetable sections, but then you're coming back to the culinary sense.

Unfortunately, when the two senses come together, people can sometimes make pretty wild claims. Perhaps because the botanical definition is scientific and precise, while the culinary one is unscientific and fuzzy, people sometimes portray the botanical definition as the "real" one. This leads to statements like "technically, fruit has seeds, so tomatoes are fruit."

But it's best to simply consider the context. Generally you'll be clearly talking about food, or clearly talking about plant anatomy. And if you're talking about food, most foods have uncontroversial categorizations, even if explaining why is difficult.

So if you want to be a smartass, by all means, when someone asks for a piece of fruit hand them a tomato and say "technically...". But if you want to just enjoy food and not get into pointless arguments, just use a bit of common sense and avoid trying to force the two senses of "fruit" together.

Botanically, a fruit has seeds.

A vegetable is the edible portion of a plant. Vegetables are usually grouped according to the portion of the plant that is eaten such as leaves (lettuce), stem (celery), roots (carrot), tubers (potato), bulbs (onion) and flowers (broccoli).

A fruit is the mature ovary of a plant. So a tomato is botanically a fruit but is commonly considered a vegetable. According to this definition squash, pepper and eggplants are also fruits. Then there are seeds such as peas which are also considered vegetables.

As a food they often get reclassified.

One factor is the amount of complex versus simple carbohydrates. Think simple - sweet - sugar. Medically complex carbohydrates are preferred as you don't spike. Nutrition is off scope for the site. What I am saying is if you group by simple versus complex it explains a lot of the common exceptions.

Tomato, cucumber, or pepper are botanical fruits that are commonly thought of as vegetables. They are all relatively low in simple carbohydrates < 2/3 of the carbohydrates are sugar.

An avocado is very low in sugar and is commonly considered a vegetable.

And apple is actually low in simple carbohydrates but most people would hold with fruit.

A sweet potato is sweet but it is still relatively low in sugar.

Almost 1/2 the carbohydrates from carrot is sugar but I would still call it a vegetable. But I would call carrot juice a fruit juice.

If you're confused by the fruit and vegetable differentiation you can remember a rule of thumb - a fruit has seeds while vegetables don't.

Even the botanical definition is a bit confusing as a 'true fruit' relates to a very species type of structure and does not include, for example apples and strawberries.

A good practical definition is that fruits are specific parts of a plant which are produced seasonally and harvested without harvesting the whole plant or to put it another way fruits are something which is 'picked'.

Clearly a big part of this is down to language, we are discussing this in English and when English developed there was a pretty clear distinction as in medieval north western Europe you had apples, pears and berries and anything else which couldn't run away was a vegetable and a lot of the confusing cases like tomatoes, peppers, squashes, cucumbers (and related) were either completely unknown or didn't travel well.

In terms of cooking there are some clear differences in their properties. Often fruits have a high moisture content (juice) and as well as being sweet may also be sharp or sour and tend to have more complex and aromatic flavours.

Really it is all about convention and the important thing is to understand the characteristics of a specific ingredient

I don't think it really matters, does it. Botanically, as already said, a fruit is any seed containing capsule (drupe, berry, nut and so on), or one that would carry seeds without the intervention of Man, so a pine cone is a fruit, along with the usual plums, apricots, courgettes (zucchini depending where you are) tomato and so on. Roots, shoots, stems, leaves, and tubers are not fruits, but are of plant origin, and many of these will be described as vegetables. How cooks decide on a description is probably entirely down to whatever they're being used for - does the addition of mango or grape to a leafy salad make it a fruit salad? Clearly, it does not. As far as cooking goes, there are definitely blurred lines between 'vegetable' and 'fruit', many often being used in both savoury and sweet dishes. So unless you feel like creating a new term or two, you're stuck with describing anything of plant origin that's served as a dessert as 'fruit' and anything served as savoury as 'vegetable', regardless of its botanical definition.

This answer is from a culinary point of view only, but I thought it worth mentioning.

I asked this of a chef I used to work with, figuring he'd know due to his education (CIA) and experience (40+ years), and this was his answer:

If you only remove the part you actually eat but leave the main part of the plant intact, its a fruit. If you actually cut off part of the main plant or eat the whole thing, its a vegetable.

By this reasoning, fruits would be things like apples, citrus fruits, stone fruits, grapes, cherries, tomatoes, eggplant, peppers, bananas, pineapple, cucumbers, and all manner of squash or berries. Meanwhile vegetables would be things like potatoes, carrots, yams, spinach, lettuce, cabbage, broccoli, cauliflower, turnips, asparagus, jicima, and onions.

A really crude definition: A fruit is something you put in your pudding/dessert or your breakfast; a vegetable is something you put in your dinner.

Apple - goes in cereal and pie --> fruit. Tomato - goes in pasta and salads --> vegetable.

Of course, this isn't perfect. Pineapple, for example.

This leads to some interesting definitions. In my country, pumpkin is a vegetable, because we roast it and make soup out of it. In North America, it is a fruit, because pumpkin pie is a dessert.