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"

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.