From Hard Drop - Tetris Wiki
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Gravity can be thought of as an automatic drop. It moves a tetromino downward into the playfield at a regular rate, which may change depending on the difficulty level. Some games move the falling tetromino down the display by a distance of one block every so often; others move it continuously by units smaller than a block. If a tetromino cannot move down further, it locks into place either immediately or, in games that use TGM rotation or SRS, after a short delay.
Gravity is expressed in unit G, where 1G = 1 cell per frame, and 0.1G = 1 cell per 10 frames. Older games cannot move the tetromino down more than one cell per frame (60 cells per second). Newer games, especially those capable of a ghost piece, can do so; play at such speeds requires a lock delay. The term 20G was coined by the developer of Tetris The Grand Master to refer to a speed of 20 cells per frame, which produces the effect of a tetromino instantly falling onto the stack as soon as it appears in the playfield.
Gravity, especially recursive gravity, can also refer to the downward motion of large groups of blocks on the playfield after a line clear.
 Soft drop
Many games allow the player to temporarily increase the gravity by holding down a key, most often Down on the directional pad or joystick. A tetromino under soft drop (sometimes called fast drop or just drop) generally falls at around 20 to 60 blocks per second, as fast as or faster than DAS. The first few generations of games on consoles had only soft drop, not hard drop. Older games will lock a soft-dropped piece as soon as it lands. Newer SRS based games apply the same lock delay used for gravity; some of these (such as Tetris DS and Lockjaw) also lock the piece if the player presses the button after the piece has landed.
 Hard drop
Hard drop (lowercase D) refers to forcing the gravity to 20G for one frame so that the piece lands instantly. Quite a few early PC games had only hard drop and no drop.
Some people use the term hard drop or sonic lock to refer to the more common version of this move that locks instantly, as opposed to firm drop or sonic drop for the less common version that has a lock delay (as seen in The New Tetris and games with TGM rotation after the original TGM). In Tetris Best, lock on drop and hard drop is an option. Tetris Best 2 does not lock on hard drop.
The "firm drop" also allows for Zangi-moves with a quick rotation of the joystick.
Hard Drop (uppercase D) refers to the name of this community as a whole.