I really like this style of dress, where the skirt sticks out a bit, and I would like to have a dress like that for prom but I don't know what it's called! Thank you!

Could be called a: short ball gown short full skirt short circle skirt and of course: strapless, natural waist (at least in this case)

I believe the puffy skirt may have a petticoat worn inside, or the dress comes with a layer of hard net sash inside skirt. You should be able to do that with any dress which has enough space at skirt :)

Cupcake style

I'd call this a strapless ballerina skater dress. It's not a normal skater dress because it 'puffs out', if you will, a lot more. It's in between a ballet skirt and a skater dress.

skater dress :)