What are the differences between a crescent wrench and channel locks?

You are using brand names. A Crescent wrench is generically called an adjustable wrench. Channel locks are known as adjustable pliers.

The adjustable wrench adjusts by means of a thumb wheel screw and has only one handle.

Adjustable pliers adjust by moving the handles apart and sliding the jaws together or apart. They rely on the user's grip strength.