Slippers are a softer shoe that younger dancers use when starting to dance. They are made out of leather or canvas. The ones in the picture are made out of leather. I prefer leather because they won't wear out as fast. Older dancers use slippers too. They are required to take at least one class with slippers.
As you can see, I've worn a hole straight through the big toe of one of my slippers. Time to get new ones!
Once dancers are old enough and are at a high enough level in their dancing, a dancer will use pointe shoes.
Pointe shoes are a harder shoe that will enable the dancer to dance on top of their toes. A pointe shoe has a hard box at the end of the shoe and a hard shank (or sole) on the bottom to help support the dancer's foot. If you are constantly on top of your toes they are going to hurt, so dancers will put toe pads in the shoe to help cushion their toes when they go on to pointe.
Another form of dance that I just recently starting taking is jazz.
Those are jazz shoes. Jazz is a form of dance that is more modern and the moves are more free form. Pop music is what is danced to. It is really fun and is something that makes me feel relaxed.
Dance is something that I enjoy doing and hope to enjoy for years to come. :)