Distance unit
A Distance unit refers to an arbitrary unit of measurement that calculates the in-game distance between objects. In the Smash series, nameless distance units are used to calculate the outcomes of interactions reliant on concrete distance.
Overview
Many aspects of video games are reliant on distance to perform specific interactions. A common term used to judge distance is the amount of pixels. Though this is technically true on the surface level, actually using pixels to gauge distance is problematic for a variety of reasons. First off, a game's pixel count can vary frame by frame depending on factors like camera placement and screen resolution, meaning the amount of pixels between objects are constantly fluxuating. In the case of 3D games specifically, the game engine does not even envision the game in terms of pixels due to technical issues that would arise doing so. This means that distance needs to somehow be measured in another way.
The most common method of measuring distance is to put an invisible grid on an entire map, and each grid space is coded as a unit. Sometimes these units are correlated to real-world units of meaurement, which can help with level design and scale. This is not the case for the Super Smash Bros. series, as the unit remains nameless throughout all games. The distance units in Smash are also cubic, being measured on the X-axis, Y-axis, and Z-axis.
Applications
The most common use of distance units is calculating the sizes of hitboxes. If hitboxes were measured by pixels, they would constantly be changing sizes due to camera placement and resolution. The units are used for consistency and fairness. Other character attributes like speed, gravity, and air friction are measured by the amount of units traveled over the amount of time spent measured in frames per second.
Melee introduced the concept of Phantom hits (officially tilted "Glancing Blows" in Brawl and onward), which is often incorrectly explained as hits being a pixel off. A phantom hit is actually activated when a hitbox and an opponent's hurtbox overlaps by 0.01 units or less (0.1 units in Brawl and onward).
The Training stage in Ultimate has a background that uses grid spaces. it is theorized that this grid measures the Ultimate distance units, though this has never been confirmed.