The main distinction is bootie or non-bootie. We call these half-foot or full-foot fins. The half-foot fin has a strap in the back that needs to be adjusted and tightened when placed on and loosened to take off. The full-foot fin is usually less bulky and has fewer parts to deal with. Simply pull it on like a sock.
After this the distinctions are endless, with marketing gurus making their fins the best, and the fastest, and the lightest, etc. Here on Utila you will be fine with any kind of fin. There is usually very little current underwater. The surface current can be harder with a strong east wind. Most people dive from boats here. Shorter fins are easier to use and keep from kicking the reef for beginners.
A fin with a bootie can be useful if you plan to do a lot of shore entries. The booties will then double as a shoe when walking over rough sand, rocks, or the deck of a hot boat. Also useful if you are diving is in colder water elsewhere in the world. The added neoprene will help insulate your foot in temperate waters.
Some fins float and some fins sink. It is a good idea to test your fins so that if you ever drop one you will know where to look for it!