Are smoothies and milk shakes the same things with different names?

For smoothies, the main body of the drink is fruit that has been blended with some limited quantity of liquid or ice. Typically, one of the fruits is banana, and other fruits (berries, strawberries, kiwi, etc.) are added for flavor. They often include a sweetener of some sort, such as honey or turbinado sugar.

Milk Shakes are typically composed primarily of milk or ice cream, and may include limited amounts of fruit for flavor. They also usually include some sort of sweetener, such as sugar syrup or malt syrup, or a flavored syrup such as strawberry or chocolate.

The general principle is that smoothies are mostly fruit, milk shakes are mostly milk. For your drink, I think it being a smoothie or a milk shake depends on the proportions of the ingredients added (i.e. more banana means smoothie, more milk means milk shake).

Based on the general principles from above, you could call your drink either a milk shake or a smoothie and be correct. That said, the original Banana Smoothie, as recorded from 1941 on this smoothie fact page, included two big ripe bananas and two and one-half cups of milk. Since that seems to be exactly what you're making, I'd say that your drink is a smoothie based on the original definition of the term.

No, they are similar, but not identical.

A milkshake is generally made from ice cream, milk, and perhaps flavoring such as chocolate syrup or a small amount of fruit, blended together as a sweet drinkable confection. Ice cream is the characteristic ingredient in a milk shake.

A smoothie is a puree of fruit and other ingredients, often one or more of including milk, yogurt, eggs, ice, and perhaps other ingredients (the variety is endless), blended together to a consistency liquid enough to drink. Fruit is most often the key ingredient in a smoothie, but almost anything goes if you can blend it and drink it.

Your banana and milk drink would be considered a smoothie, but not a milkshake due to the lack of ice cream.

Caveat: I have described how these words are used in North America... it may be that elsewhere they are used differently.

I think that's a smoothie, but if you put ice cream in there you'll have a milk shake. :)

It is actually a milk shake for sure. Smoothie would never contain high amounts of liquid content.