Grab range refers to the portion that will be covered by a throw hitbox once it starts up.
If the throw hitbox overlaps the opponent’s throw-taking hitbox, the throw comes into existence.
Many throws only have an extremely short opportunity to grab (often only 1 frame), so it is easy to understand grab range in terms of “I can only grab if I put out the move at such and such a range”.
Most throws will not happen when only one party is in midair, so the idea of “range” makes perfect horizontal sense, but air throws also have a vertical aspect to them, so there may be a little confusion there.