What is the difference between boiled vegetables and stewed vegetables?

The distinction is not so much what you add as what you do with the liquid. If I am making boiled carrots, when they're done I drain them, throwing the water away or possibly saving it to make soup with some other time, and serve the carrots. If I am making a vegetable stew then not only do I add things to the liquid (to flavour or thicken it, or both) but I keep the liquid, and serve the vegetables and liquid together in a bowl.

The words are not really comparable. They are rarely used as adjectives, actually. But when they are, their meaning can overlap or also not overlap.

"To boil" is primarily a verb. It denotes the process of cooking vegetables by immersing them in water at roiling boil.

"A stew" is primarily a noun. It denotes a kind of meal which has a liquid component, but not enough to count as a soup, has a mixture of many solid components in smallish pieces (you don't need a knife to eat it), and has been cooked for a long time, until everything is quite tender (especially if there is meat in it).

Preparing a stew could, in principle, involve boiling on stovetop. But tastewise, it turns out better if you use other techniques, such as simmering on stovetop or baking it in an oven.

"Stewed vegetables" is a construction which the language allows, but it's not really common. On a menu, you'll see "vegetable stew", not "stewed vegetables". If somebody would serve them nevertheless under this name, you'd really expect to get the whole stew (soft vegetables + liquid, as Kate Gregory said), and not only the vegetables alone.

"Boiled vegetables" is also rather unusual. It is the word a cook would use if a more specific one isn't applicable. For example, chefs rarely or never say "boiled vegetables" when using blanched vegetables, even though blanching is a special type of boiling. It is so unspectacular and connected to memories of bad cafeteria food that restaurants don't use it on a menu, frequently opting to leave the descriptor out altogether where it would have been applicable. You get "lamb ribs with peas and mint sauce", not "lamb ribs with boiled peas and mint sauce".

But because "boiled" is used when nothing more specific is available, if you happen to see it, you can really expect to get "naked" boiled vegetables, not stewed, creamed, or prepared by another method which involves boiling.

Taking some inspiration from here, I would guess the difference has to do with the way they're cooked.

Boiled vegetables are tossed in a pot of water (brought to a boil), and are done as soon as they become tender. They are usually preferred a bit crisp, al dente, and if overcooked would be watery and flavorless, and are intended to be prepared and eaten quickly.

Stewed vegetables, well - as mentioned in the above link, stewing is a slow, moist-heat method of cooking. A vegetable, stewed, would be cooked for much longer, and probably at a lower temperature - perhaps a simmer, or baked. The goal would be a softer vegetable, with concentrated flavor.

Additionally, I would assume that a vegetable described as boiled was simply cooked in water, with perhaps a bit of salt. Boiling is quick enough that other flavors wouldn't penetrate very far before the vegetables are drained (and if the water is retained, that isn't boiled vegetables but soup), so boiled vegetables are usually seasoned once they're out of the water.

Stewed vegetables would be more likely to be seasoned - low, slow cooking methods are quite good at infusing and melding flavors. This may partially explain why you saw the addition of other seasonings as a difference between the preparations - though aromatic vegetables may season those cooked with them even without other herbs or spices. Stewed vegetables may improve in flavor the longer they are cooked or let stand, as the flavors concentrate or meld, and are probably descendants of recipes meant for long cooking and large numbers.

And, since others have mentioned vegetable stew... I think that is again something different. Stewed vegetables emphasizes the vegetables, while vegetable stew emphasizes the whole dish. A stewed vegetable may be drained, or have a much higher proportion of solids to liquids - think vegetables in gravy vs soup - or be only one or two vegetables (stewed carrots, stewed turnips, stewed tomatoes). I would assume a stewed vegetable is primarily that vegetable and/or intended as a side dish or an ingredient in a larger recipe. A vegetable stew is usually many vegetables, balanced for flavor, and is usually a main course.