Open heal:
These type of fins have a strap at the heal to hold the fins on. They can be made of various materials, but the more expensive ones are more comfortable due to the quality of materials. Open heal are also designed to be used with boots or wetshoes. The exception to this is Hydrosplit fins that are designed to be worn without boots.
Full Foot: Designed to be worn without boots. They are better suited to warmer waters and ideal for snorkeling. Again the more expensive fins are made from better material and therefore are more comfortable.
Split fins:
These fins are designed to provide a smoother movement and are able to transmit power through the water more efficiently. Basically that means its easier to snorkel and less tiring. This type of fin is generally very expensive.