"Billiards" was the original game on what we would call a snooker table. Snooker was not invented until the second half of the 1800s, and tables existed long before then. The usual form that was played in championships from about 1840 to 1940 is with three balls -- two cue balls and a red ball. There are several ways to score, including scratching and caroms. The English, being the perverse creatures that they are, insist on calling those "in-offs" and "cannons".
Old-timers will still call a 12-foot table a "billiards" table and may use the generic term "billiards" for any game played on it.
Tolkien likely played the 3-ball game.
If you're interested, search out "Walter Lindrum" and/or "English Billiards" on YouTube. English billiards is a great game and has a lot to teach those who are willing to learn.