POOL

21/4" are the standard size balls.

On coin op tables when a mechanical system is used, the cue ball is larger in order it be returned when scratched.
In pool most games, 15 balls plus the cue ball are used, except for 7 and 9 ball.

SNOOKER

Ball sizes are most commonly 21/16" (English) and or 21/8" (American).

In most snooker games, 15 red balls PLUS numbered balls 2 through 8 and a cue ball are used.
English snooker balls do not have numbers on the "colored" balls.  American balls are numbered as well as colored.  Both sizes are available in both styles. 

 Left:  21/4" #1 Pool ball

Right:  21/8" #2 Snooker ball