Not at all clear what you mean, please explain. All I was saying is that "solids and stripes" is the same as "8-ball" not that either one of those names had anything to do with snooker.
There's lots of different variations, I've played two types, one on a snooker table with 3 balls and one called "Bar Billiards" (often played in pubs). The latter is played on a table with holes in the surface each one protected by a pin.
"Billiards" has become a generic term, there are carom billiard games, played on a table with no pockets; and pocket billiard games, obviously played on a table with pockets. A 3 ball game on a snooker table is new to me though.