If so, they are the leather straps that go round the top of a leather riding boot and were originally intended to keep the breeches in place. Now (with the advent of stretchy material and velcro!) they are purely decorative. They are worn with hunting style straight top boots and not dressage cut boots.
If there really is something called a gaiter strap, I have no idea what it is for!
A garter strap was always used with long boots to put through the buttons that were on breeches to help keep them in place, not really used now as breeches are not made of the material they used to be. It is still traditional to wear them in the show ring and hunting.