Are billiard balls different to snooker balls?

The correct answer is "maybe". The original game of billiards refers to English Billiards and this is nothing like pool. English billiards uses balls that are 52.5mm (2-1/16 inches) in diameter. The Carom Billiards games, such as Three Cushion, is also nothing like pool. Carom billiard games use balls that are 61.5mm (2-7/16 inches) in diameter. Both English and carom billiard ball sets use 3 balls: a white one, a red one, and another white one with a spot on it (sometimes substituted with a yellow ball).

However, the term billiards today nearly always refers to the Pocket Billiards games, most likely 9 Ball or 8 Ball. These are also referred to as pool games and all use the same balls. These balls are 57.15mm (2-1/4 inches) in diameter. There are 15 numbered balls and a white cue ball in a typical set.