The Call of Duty 4 remaster is closer to being a full-blown remake. You can see some shared assets if you look closely, but it's a significant overhaul of assets in addition to running on a newer version of the engine.

It looks better, it feels better, even with its occasional audio issues. Still, it is a bit short, and unless you are a true fan or just nostalgic about those days you played it, it is hard to recommend to anyone else, due to its lack of multiplayer and lack of longevity.