Hi Daniel, welcome to GM

 Hybrid clubs are just that, a cross, (or hybrid), between an iron and a wood, some look like irons with large, chunky cavities behing the clubface, others look like mini woods. Many people find them easier to use and more versatile than their equivalent irons/woods due to the shorter shaft lengths and lower center of gravity.

You can use Hybrids for anything really, obviously they are primarily designed for longer shots, but they are equally useful for little chips and bump and runs around the greens and for popping the ball out of the rough. I used to carry 2 hybrids in place of the more traditional fairway woods and they were awesome off the tee as 'driving irons'.

I would suggest trying out a few and comparing them to whatever clubs they correspond to in your own bag, if they work better, they are probably worth considering.

How much do they cost? How do I tell what clubs they correspond to?

 Are rescue woods classed as hybrid clubs?

Rescue, hybrid, utility - doesn't seem to be any difference between them.

The hybrid club has been around for a long time (e.g. the Cobra Baffler) but TaylorMade are credited with having made this type of club popular in recent years with their "Rescue". So now the term rescue is used interchangeably with hybrid/utility (a bit llike any digital music player is called an MP3, even tho MP3 is simply a music format).