In baseball, a foul tip is defined as "a batted ball that goes sharp directly from the bat to the catcher’s hands and is legally caught. A foul tip is considered a strike and the ball remains "in play."
A foul tip is not the same as a foul ball, although many people mistakenly use the term to refer to any pitch at which the batter swings and makes slight contact, regardless of whether it is caught by the catcher. However, the rules are very narrow: it is not a foul tip if the ball touches anything else on the way to the catcher's hand or glove or if it is not legally caught and held. Anything else is technically a foul ball, including if the ball is caught after popping up into foul territory.
The rules treat a foul tip as equivalent in every respect to a pitch at which the batter swings and misses.
In contrast, a foul ball is not always considered a strike. Specifically, a batter with two strikes against him or her who hits a foul ball is not automatically out.