pubs tend to have pool tables rather than either billiards or snooker

Indeed they do. Though there's a fair amount of bar billiards played hereabouts. I'll have to find a link for this, as an explanation would be complex!

I know of quite a few snooker clubs, but I don't actually know of any billiard clubs. Isn't the same size table used for billiards as snooker?

Beastlified if I know.