The tag wiki on this website says:
For questions about the d20 System, an RPG system originally published in 2000 by Wizards of the Coast. The d20 System was developed alongside D&D 3e and is a derivative of it, but it forms the mechanical backbone for a variety of RPGs entirely departed from the D&D system.
And the wiki page says:
The d20 System is a role-playing game system published in 2000 by Wizards of the Coast, originally developed for the third edition of Dungeons & Dragons.1 The system is named after the 20-sided dice which are central to the core mechanics of many actions in the game.
Much of the d20 System was released as the System Reference Document (SRD) under the Open Game License (OGL) as Open Game Content (OGC), which allows commercial and non-commercial publishers to release modifications or supplements to the system without paying for the use of the system's associated intellectual property, which is owned by Wizards of the Coast.
It looks, at least to me, to be more of a trademark/legal matter than just using a d20.
But in any case, which roleplaying systems are derived from the d20 System?
It looks like D&D 4E is not covered by it, or at least the associated OGL, but I appreciate they are not the same thing. Whereas stuff like Pathfinder and d20 Modern do seem to be derived from it.