Billiards is played with three balls: white, red and yellow. The white and yellow balls are the cue balls of the two opponents respectively and the objective is to score some set points. The player who scores the required points first, wins.
In snooker, there are 15 red and six coloured balls and one cue ball. The player has to pot a red first, then a colour, and again a red, and so on. At the end of the frame the player with more points wins.
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Billiard tables have larger pockets and use slightly larger balls than snooker. Other than that the tables are very similar in size and design. The smaller snooker balls are red, and yellow with white cue balls. They are not numbered like billiard balls and the game is entirely different than say 8 or 9 ball played in the USA. A billiard table can be converted to snooker because you can make the holes smaller to accommodate the snooker balls, but not vice-versa.
In snooker you keep score and after all the balls are potted it is the one with the highest score that wins. 147 is the maximum score but theoretically 155 is possible. With billiards an infinite score is theoretically possible. In pool it is ho pots all their balls and the black first that wins.