The disciplines of carom billiards
Carom billiards isn't a single game: it's a family of disciplines that share the same table and the same three balls, but not the same way of scoring points. This site mainly teaches straight rail, one-cushion (One-cushion system) and three-cushion (System 4, Conti system) — here's the overview. To find out where it all comes from, head to a bit of history.
The disciplines
Straight rail (partie libre)
The learning format: every contact of your cue ball with both object balls scores a point, with no cushion requirement. See the detail in Rules of the game.
Balkline (47/1, 47/2, 71/2)
Lines drawn at a fixed distance from each cushion divide the table into zones: once a quota of points scored within the same zone is reached, a ball must be sent out of it. Three widths exist — the quotas are detailed in Rules of the game. A late invention: balkline was created in the 1880s to contain a scoring technique that let players run up points almost endlessly in straight rail (see the history).
One-cushion
The cue ball must touch at least one cushion before the second contact. This is the system taught on this site under the name One-cushion system.
Three-cushion
The cue ball must touch three different cushions before completing the carom — the most technical and most widely followed discipline in carom billiards. Two calculation methods are taught here: System 4 (one reference cushion) and Conti system (four cushions).
Artistic billiards
Set shots (direct carom, bricole, casin...) to be completed a fixed number of times, on precise ball positions. A discipline of pure precision, judged on whether each shot succeeds rather than on a running score.
Five pins (Italian billiards)
Five pins (one red, four white) arranged in a cross (the "castle") at the centre of the table: each shot combines points from knocked-over pins and caroms. Very popular in Italy and Latin America, also played competitively in France.