What are the differences between cowboy style horse riding and normal horse riding?

Cowboy style horse riding is considered Western riding there are several different events for a western rider...trail, endurance, rifle endurance, pleasure, equitation, rodeo, gymkana, reining, ropeing, barrel, etc....

Another Type of Riding Is English Riding which is ridden in a saddle without a horn as some people say under English there are several different types of English riding

dressage, side saddle, jumping, hunters, fox hunting, hunter paces, equitation, pleasure, trail, Australian stock seat, saddle seat, 3 day eventing, horse trials, etc....

Depending on your preferance is what one would consider normal...