According to the owner and moderator of billiardsforum.info:
"Hah the answer will probably suprise you. "Billiards" is a term which describe all games that are played on a billiard table. The real name for what we call pool is "pocket billiards".
"Pocket Billiards" is just one version of Billiards. Some billiard games are played on tables where pockets don't even exist, such as 3 cushion or bar billiards.
In the 19 century "poolrooms" existed, but were not the pool rooms that we know today. They were simply betting parlors where people came in to bet on horse races or play poker. They were called "poolrooms" because everything involved a "pool" of money.
While people sat around the pool room and waited on results, they installed pocket billiard tables. People of course began to gamble on these too. Therefore, the name "pool" became attached to billiards simply because of the betting, and it has nothing to do with actually playing the game. When people say something like "Hey, want to play some pool" we all know that they are referring to billiards, but technically they are asking you if you want to play a bet."
Clear as mud, eh? This is way more that you really wanted to know, right?
Yes way more! Lol!