Carom billiards and pool are two types of cue sports or billiards-family games, which as a general class are played with a stick called a cue which is used to strike billiard balls, moving them around a cloth-covered billiard table bounded by rubber cushions attached to the confining rails of the table.
Carom billiards (often simply called "billiards" in many varieties of non-British English) is a type of billiards in which the table is bounded completely by cushions, and in which (in most variants) three balls are used.
Pool, also called "pocket billiards", is a form of billiards usually equipped with sixteen balls (a cue ball and fifteen object balls), played on a pool table with six pockets built into the rails, splitting the cushions. The pockets (one at each corner, and one in the center of each long rail) provide targets (or in some cases, hazards) for the balls.
Some games do not fall into those two broad categories, most notably snooker, which, although using a table with pockets, is not part of the pool family of games, and English billiards, which features both carom and pocket scoring, and uses the same table as snooker.
Skill at one type of billiards is widely applicable to the other, but expertise usually requires at least a degree of specialization.