It depends how mod is made. If it depends on a base content of a game, it’s generally a mod for that game. That’s what Counter-Strike and DOTA for example was at first (they required Half-Life, and Warcraft 3 base files respectively).

If you make a game for a specific engine, it’s generally considered as a standalone game, not a mod. Also in olden days code for the engine and the game wasn’t separated so you couldn’t easily reuse the game engine. AFAIK Id Software was one of the first companies that made reusable game engines that were also licensed to other companies, and even made map editor available for free.