Billiards in a nutshell is playing pool, but there are a lot of different types of games to be played in billiards. Some of the most famous of these are 9-ball, 8-ball, snooker, One Pocket and Cut Throat. Depending on where you are from will determine the most popular for your region, I think 8-ball and 9-ball has the others beat though.
There is another billiards game played here in the United States known as Straight Pool or Fourteen and One. Back in the day this used to be the most popular game. This game takes a long time to play and involves clearing many racks to end one game, which could cause a game to last a very long time.
Eight Ball has became a very popular billiards game due to the bar scene, as most sports bars have a pool table or two, sometimes more. There are many different rules to Eight Ball depending on where you are from but the basics is you have fifteen balls, the last one being the eight ball, one person gets stripes the other gets solids.
One of my favorite billiards games to play is nine ball. This is a game that is very fast paced and the object is to sink the nine ball in at any time. The trick is that the cue ball must hit the lowest ball first.
Hardcore pool players like to play One Pocket for money. This is definitely a game of strategy. The game uses all fifteen balls and each player has one of the bottom corner pockets. The game ends when a player legally pockets 8 balls in his or her pocket.
If you want to play a billiards game where three can play at once, than Cut Throat is the game for you. Each player has five balls that are theirs, and the objective of the game is to hit in any ball but your own, the last person that has one or more of their balls on the table wins the game.
There are many other games in pocket billiards. You could visit Wikipedia and do a search for billiards game for a pretty complete list. These are just some of the more popular ones that you will find. At Wikipedia you will find details and rules of every game.