Team Fortress Classic is based on Team Fortress which was a Quake mod. In 1999, Valve hired the Team Fortress Quake modders to port their game to the GoldSrc (HL1) engine.

Heh. What do you think "classic" means when it's part of the title of a product? It means that it's a derivative of something else, and wants to capture some reflected glory. Don't go thinking that "Mary Shelley's Frankenstein", the 1994 movie, is the original.

Team Fortress was a mod for Quake before HL1 was a twinkle in Gaben's eye. TFC was someone saying "that sure was a fun gameplay mode, but I can't get anyone to load Q1 any more... maybe I'll recreate the same thing over again"