The smallest unit of measurement in StarCraft is pixels, but on this page and other Liquipedia pages, it will refer to cells .
Range is the distance a unit can fire at its target from its current position. 0 range, such as on the Zergling is often referred to as Melee Range. The Siege Tank is unique in that in Siege Mode it has a Minimum Range, meaning it cannot fire at targets that are closer than said minimum range. Range is also the distance units can see and reveal the fog of war and black mask as well as reveal cloaked or burrowed units if they are a Detector.
The range that a unit uncovers black mask and reveals fog of war is it's sight range. A unit cannot reveal terrain if they are on certain tiles. If a tile they would reveal has a higher height then them, then they won't reveal that tile from where they are standing. Alternatively, if the tile they are on is lower, then they will reveal it. An example of this is if they are on a lower cliff level. Certain doodads can also block sight. This can also be applied to detection range, though it is independent from their actual sight range.
These images demonstrates how tiles themselves block sight, not just "cliff height":
The shortest unit of measurement. 1 range in-game is equal to 32 pixels, while 2 range in the actual data is equal to 32. This way, a unit can have 3 range in the data being equal to 1.5 range in-game, 5 equal to 2.5, 7 equal to 3.5, and so on, which ends up being 48, 80, and 112 pixels.
Cells are a larger unit of measurement that are used on the Wiki. A Cell is 32x32 pixels large. This makes it very easy to make all measurements use a similar idea, such as 1 speed = 1 cell per second = 32 pixels per second = ~1.344 actual pixels per Logical Step in the data which can then be related to 1 range = 1 cell = 32 pixels as something similar.
Leash Range determines how far away a Hanger Unit, such as an Interceptor, can be away from it's Host Unit, such as a Carrier. If they get further away than the Leash Range distance than they will want to return to or get back within Leash Range to their Host Unit before performing any other action, such as attacking.
A unit's collision box is measured in pixels from the center of the unit. There are 4 offsets: Left, Right, Up, and Down. Left and Up consider 0 as part of their measurement. For example, the Lurker's offsets are 15 for Left, 16 for Right, 15 for Up, and 16 for Down, but is actually physically 32x32 pixels. Units generally do not want to get within another unit's collision box and will try to separate from each so their collision boxes do not overlap. Units will sometimes overlap regardless and when this happens they will try to separate. Usually when this happens, they will not receive orders until they are separated and no overlapping collisions are taking place. Here is a list of every unit and building's collision hitbox.
Movement speed in-game is physically measured in pixels per Logical Step, however on this Wiki, it is measured in Cells Per Second. To clarify, this is ((Pixels * 1000) / Delay) / 32. On the Fastest game speed, "Delay" is 42. A list of all of the unit's pixel per Logical Step listings can be found here and a list of all Game Speeds and their respective millisecond delays here.
Area of Effect
Area of Effect is also listed in actual pixel distance, like Movement Speed. Like Movement Speed, it will also be measured in cells. This is simply pixels / 32. Area of Effect functions in three zones. Each zone has a hard-coded Fall-Off. The first zone, that we will just call Inner, deals 100% of the weapon or ability's damage. The second zone, Medium, does 50%, and the final zone, Outer, does 25%. The Spider Mine has a very impressive splash radius of 50 pixels (1.5625 cells) for Inner, 75 pixels (2.34375 cells) for Medium, and 100 (3.125 cells) for Outer.