Sports jackets are called sports jackets because they were first worn for watching sports like horse racing.
A sport coat, also called a sport jacket, is a men's lounge jacket designed to be worn on its own without matching trousers, traditionally for sporting purposes. Styles, fabrics, colours and patterns are more varied than in most suits; sturdier and thicker fabrics are commonly used, such as corduroy, suede, denim, leather, and tweed.
Originally, sports coats were worn as appropriate attire for participating in certain outdoor sports. With time, they were adopted by those attending such events, and came to be used on more formal occasions.
A shooting jacket is a type of sport coat worn, as the name suggests, originally while participating in the sports of shooting or hunting. It usually comes with a leather patch on the front shoulder to prevent recoil wear from the butt of a shotgun or rifle, and frequently has matching leather patches on the elbows.
A hacking jacket is a wool sports coat for casual horseback riding, often of tweed and traditionally 3 buttoned with a single vent.
A blazer is similar to a sports coat, typically tailored from solid color or striped fabrics. Blazers are often made with metal buttons reflecting their origins in the British Navy and the sport of boating, though this is not necessarily a defining feature. Blazers also often have patch pockets, unlike other kinds of coats.