Nowadays, pool game equals pocket billiard game. Playing pool means
playing some type of billiard game whereby the goal is to pocket the
object balls following the specific game's rules and restrictions.
Apparently, in the not so far past, the term "pool" actually referred
to the billiard games played on pocketless tables, known today as carom
billiards.
The name "pool" is derived from the original setting of
the game. In 19th century America, pool games used to be played in
poolrooms, which were gambling parlors that hosted horse racetracks and
the billiard tables kept the bettors entertained in between races. Heres some extra reading.