Definitions:
Billiards: Any of several games played with hard balls of ivory or of a similar material that are driven with a cue on a cloth-covered table enclosed by a raised rim of rubber, esp. a game played with a cue ball and two object balls on a table without pockets
Pool: Also called pocket billiards. any of various games played on a pool table with a cue ball and 15 other balls that are usually numbered, in which the object is to drive all the balls into the pockets with the cue ball.