This is a soft box. When used the soft boxes softens the light and makes the light look a lot softer and more natural on the object of person. It is a indirect light meaning the light won't be focused on a single thing it will light up the frame. The light reflects on the inside wall and the comes out of the fabric which gives it the soft look.

This is a small reflector light. This covers the light just a little bit it reflects it. It is still a direct light as it focuses on one part of the set. It is usually used on the main person or object in the set.
This is a snoot. This is a harsh light. This light is like a spot light it is the most direct light you get and the harshest. The snoot is usually used on a persons face or a object.
This is a backdrop. A backdrop can come in various colours. this is used as a background of a set and every studio will have one.
These are barn doors. you would attach these to a small reflector light. These make drift light and you can choose what shape you want it. They all move so it can be really direct or not to direct.