In baseball, a batted ball is any ball that, after a pitch, is contacted by the batter's bat. One or more of several terms are used to describe a batted ball, depending on how it comes off the bat and where in the field it lands.
There are generally three descriptive categories for balls hit in the air:
A ground ball or grounder is a batted ball that rolls or bounces on the ground. A line drive in the infield may become a hard grounder to an outfielder; these are usually called line drives regardless.
Bunts are generally not considered to be ground balls; they are a distinct type of batted ball, where the batter, in effect, tries to 'block' the ball with the bat held steady, rather than taking a full swing.
Any of the above types of balls might be fair balls or foul balls. Umpires will also signal first signal fair or foul on fly outs near the foul line, but the result of a foul fly out (or foul out) is no different from a fair fly out; it is not a foul ball.
A foul tip, a very different type of batted ball, is a ball tipped off the bat which goes sharply and directly to the catcher's mitt or hand. If the catcher does not catch the ball, it is an ordinary foul ball. If the catcher has to move either his mitt/hand or body to catch the ball, it is not a foul tip, as the ball would no longer have traveled directly to the catch. However, if the ball deflects from either the mitt or hand and is subsequently caught before landing, it is still a foul tip. A foul tip is always a strike, and is a strike out if there are two strikes on the batter. The foul tip is a live ball and runners may advance.