You have two main types;
Fulcrum
Non-fulcrum.
Fenders, whether they use the traditional 6 hole or two post configuration use the fulcrum principle that when depressedl, both loosens the strings and raises them.
Floyd Rose is an enhanced fulcrum designed to minimize the possibilty of detuning.
Fulcrums are spring-adjustable.

Non-fulcrum designs include cams, rollers and other variations that don't raise the strings as they are loosened.
On the whole, these are more expensive, almost all require routing, and do not have the same action associated with fulcrum designs.