In Billiards, the maximum score is 81 (possible only if you sink all 9 balls on the break), and it subtracts 3 points for each additional shot. So my 63 points would be for sinking all 9 balls in 6 shots. I have no idea why it's backwards like that.
In multiplayer, the score is the total point value of all the balls you sink, so the maximum possible score is 45.
Fouls subtract 3 points each in both modes.