[Warrenkicker]

MJT did answer your question. NFL - punt required after safety. NCAA and NF - punt or free kick allowed. No holder required. Kickoff from standard kickoff tee.

The difference between a punt and a drop kick is that a punt never touches the ground prior to being kicked. A drop kick touches the ground before or as being kicked.

2-23-3 A free-kick is any legal kick which puts the ball in play to start a free-kick down. After the ready-for-play signal and before the kick, each player other than the kicker and holder for a place kick must be behind his free-kick line. A free-kick is used for a kickoff, for a kick following a safety, and is used if a free-kick is chosen following a fair catch or awarded fair catch.
ART. 4 A scrimmage kick is any legal kick from in or behind the neutral zone. Either a place kick, punt, or drop kick may be used. For a place kick, the ball must be controlled on the ground or on a legal kicking tee by a teammate.
ART. 5 A kickoff is a free-kick which puts the ball in play at the beginning of each half of the game, after a successful field goal and after any try. A place kick or a drop kick shall be used for the kickoff.
ART. 6 A drop kick is a legal kick by a player who drops the ball and kicks it when it touches the ground or as it is rising from the ground. A drop kick may be used for a scrimmage kick, a kickoff, a free-kick following a safety or for a free-kick following a fair catch or awarded fair catch.
ART. 7 A place kick is a legal kick made while the ball is in a fixed position on the ground or on a kicking tee. No material or device may be placed on the ground to improve the kicker’s footing. The ball also may be held in position on the ground or on a kicking tee by a place-kick holder who shall be a teammate of the kicker. A place kick may be used for a scrimmage kick, a kickoff, a free-kick following a safety or for a free-kick following a fair catch or awarded fair catch.
ART. 8 A punt is a legal kick by a player who drops the ball and kicks it before it has touched the ground. A punt may be used for a free-kick following a safety or for a scrimmage kick.

So a scrimmage kick which is not a punt or drop kick must be controlled by another player either on a tee or on the ground.