> A question for people who know this sort of thing: does a billiard have anything to do with the game of billiards?

The billiard was named after a bet between its inventors.
They were two people from Cardiff who were migrating to the USA about in 1880; their journey was rather boring, so they started thinking of a new game that could have been played either for fun or to bet some money.
They invented the game and started playing, betting twice the win at each round, while thinking about a name for their creation.
After some hours, the bet grew up to about 1,000,000,000 pounds so spectators started calling for it crying "the milliard" or "the billion", following their usual denomination.
At this point, the two players stopped and looked in amazement at each other until the youngest of them said "Hey, this is a billiard!".

Well, if you believed to the ThunderHamster, why can't you believe this...?

AP.

(Actually, billiard comes from the original Italian name of the game which in turns comes from the Latin/Ancient Italian for 'ball':
ball (if made of hard material)-> 'bilia'
game with that kind of balls -> 'biliardo' which
was translated as 'billiard'.
I don't remember when it was invented, but it has
a century-long tradition and exists in about five
different styles, plus the 'American' one which is
that with colored and numbered balls and holes at the corners of the table).