Billiard cloth (sometimes erroneously called felt) is a specific type of cloth that covers the top of the tables "playing area". Both the rails and slate beds are covered with 21-24 ounce billiard cloth (although some less expensive 19oz cloths are available) which is most often green in color (representing the grass of the original lawn games that billiards evolved from), and consists of either a woven wool or wool/nylon blend called baize.
Most bar tables, which get lots of play, use the slower, thicker blended cloth because it can better withstand heavy usage. This type of cloth is called a woolen cloth. By contrast, high quality pool cloth is usually made of a napless weave such as worsted wool, which gives a much faster roll to the balls. This "speed" of the cloth affects the amounts of swerve and deflection of the balls, among other aspects of game finesse. Snooker cloth traditionally has a directional nap, upon which the balls behave differently when rolling against vs. toward the direction of the nap.