What is the name for the type of horse racing that involves horses galloping at high speeds?

The type of horse racing involving horses galloping at high speeds is Thoroughbred racing.

Thoroughbred racing uses the Thoroughbred, a horse breed developed specifically for racing and known for a combination of speed, stamina, and competitive athleticism. Most familiar flat races, including major events such as the Kentucky Derby, Preakness Stakes, and Belmont Stakes, are run by Thoroughbreds carrying jockeys at a gallop over a prepared track.

A common mix-up is confusing the breed with the general activity. “Horse racing” is the broad sport, while Thoroughbred racing identifies a major racing category based on the horses involved. Quarter Horse racing also features extremely fast galloping, especially in short sprints, but it is associated with the American Quarter Horse and is a separate discipline. Harness racing is different because the horse pulls a sulky and competes at a trot or pace rather than a gallop.

Thoroughbred racing developed from organized British racing traditions and became a major international sport, with famous races held in Britain, the United States, Australia, Japan, and many other countries.