Movement

Synchronous smooth movement

Term “smooth movement” refers to the visual aspect of Boulder Dash games that employ smooth transitions of objects between tiles. Not to be confused with asynchronous movement.
In BD games the playfield is split into a grid and all objects always occupy one tile, kinda like chess pieces. No object is ever in-between tiles. However some games use renderer tricks to create an illusion of smooth transitions between tiles, but under the hood in the game’s model objects snap instantly between tiles when they move.
The original Boulder Dash from 1984 had no smooth movement, so the renderer accurately depicts the internal state of the game model. It always takes 1 tick and 1 frame for objects to move to adjacent tiles.
The number of ticks per second basically defines how many tiles per second a moving object can traverse. Boulder Dash has variable game speed that is connected to cave difficulty, so there is no one official movement speed. Fastest caves have 12 ticks per second, while the slowest have 3 ticks per second. Fan-made level editors use 7.5 ticks per second as a default when a new cave is created.
Slower speeds would make it easy for players to notice that Rockford can’t start moving instantly, but only when the next tick is calculated. For modern players this can feel unresponsive, laggy and cluttered, but developing this internal metronome is part of the skill that goes into BD gameplay. Faster caves make this effect less apparent.
Emerald Mine was the first BD clone that successfully created the illusion of smooth movement.

Asynchronous smooth movement

Asynchronous movement is a feature of some BD clones that allows non-synchronous transition of objects between tiles on the playfield.
Supaplex was the first BD clone to employ asynchronous movement. Combining it with smooth movement created a very responsive gameplay. The intended game speed for Supaplex is 35 ticks per second. At worst the input delay is around 28 milliseconds and 14 milliseconds on average. Input lag starts to become noticeable for most people around 50-100 milliseconds, which places Supaplex input delay way below threshold of noticeability.