The word billiards is a kind of general term describing assorted types of cue sports - games played on a table with a cue stick and pool balls. Depending upon what part of the world you are in, the games can be somewhat different. Table configurations also vary, with some being different lengths and some having pockets and others not.
In the US, the word pool is often used to describe the most popular games, such as 8-ball, 9-ball, one-pocket, and straight pool. Pocket-billiards is another term used to identify these games that use tables containing pockets.
In England, games that are played on tables without pockets, such as three-cushion-billiards and balkline, are more popular than in the US. These are sometimes referred to as carom games, because instead of sinking balls into pockets, the balls are caromed off of each other and the rails, according to the rules of the various games.
Snooker is another game that is more common in England. This game uses a large table with pockets, but the rules are much different than any of the American pool games. The balls are not numbered, and they are made in specific colors, which stand for the number of points the shooter can earn by sinking them in the correct order.
The following snooker video is a fantastic example of some excellent shooting, by a player who runs the entire table, according to the rules of this game. It's referred to as a "maximum break", and you will be hard-pressed to find a prettier example of a well-played billiards game.