Surprisingly, this is a question I get a lot: do I (or can I) wear ballet shoes in barre class? I understand the confusion: barre classes are a blend (supposedly) of ballet, Pilates and Yoga. However, the floor is either a thin carpet (ugh, Pure Barre, Dailey Method, why???), or more likely, a smooth hardwood floor that is great for a fitness class, but not so much for ballet shoes, which will slip.
You might be thinking "hey, my soft shoes will work" but nope, that isn't true. You will slip. Barre class takes place on the smooth floor for most of the class, and an exercise mat for part of it.
Socks with grip are a must, OR you can get away with barre workout "shoes". (Yes, there is a loophole: these shoes can be used for Pilates, Yoga or barre, but never for ballet).
In ballet you do not want to be gripped to the floor; in barre class you do. You will never do turns or pirouettes in a barre class (unless it is a ballet barre class in a ballet studio, but really, that is unlikely). Confusing, I know! As for bare feet, some studios might allow this, but most don't (and really, you do not want to slip in someone's sweat. It's gross).
To keep things simple, here are two graphics for you:
1. What to wear to barre
2. What to wear to ballet (this is for general, beginning ballet. If you're in an advanced pointe class, etc, this graphic isn't for you!)
And that's it! If you still have questions, get at me!