Technically, a "free kick" is any kick that is not a scrimmage kick. In other words, any time the ball is put into play by kicking, and the ball is not snapped on a normal scrimmage down, it is a free kick. This includes kickoffs, as well as kicks following a safety or fair-catch.
The kick following a safety is unique because it is the only type of free kick where the kicker has the choice of punting the ball or kicking it off a tee. (In fact, they could dropkick it as well.) Because of this, many people mistakenly think that "free kick" means the kicker can choose how to kick the ball, when in fact that is only true of the free kick after a safety.
The normal rules for kickoffs apply to all free kicks: The ball must travel 10 yards before the kicking team can recover it (unless first touched by a receiver), and it must not go out of bounds.
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