1) When I want to contribute to a project, make some local changes and offer them back to the mainline, I fork. My fork is a pseudo-throwaway thing; it contains code that is hopefully destined either to make it back to mainline, or likely to be abandoned if mainline moves on in active development.
2) When I want to go my own way with a project, using it as a starting point for a new direction of development that may wander in a direction quite far from the original (it might get renamed, it might continue development of the original becomes abandoned, etc.), I also fork.
Numerically meaning 1 is surely far more common, so it makes sense for the GitHub features and permissions etc., to optimize for that case.
Meaning 2 is closer to the original idea of a fork, from open source vernacular long predating GitHub.
Naming is hard, and I don't blame them for picking a single name for these two technologically similar (but socially different) scenarios.