The Team Fortress Classic Engineer is seen with a young Team Fortress 2 Engineer, suggesting that he was his role model.
In the Team Fortress 2 comic series, the Engineer's legs are replaced with robot legs.
A server setting allows the Spy to turn invisible instead of disguising. This is similar to the cloaking mechanic in Team Fortress 2.
The Medic, along with the Civilian class, are the only classes from Team Fortress Classic the haven't appeared in the Team Fortress 2 comic series.
The Crowbar weapon is used by every single class except for the Medic, Engineer, Spy and Civilian classes. It is still referred to as an axe in Team Fortress Classic's game files.
According to the Team Fortress 2 catch up comic, Team Fortress Classic takes place in the 1930's.
Unlike Team Fortress 2, Team Fortress Classic contains several references (and re-used content) from Half-Life, the most striking of which was the Hunted map. Instead of being a remake of the original Hunted President from Team Fortress, it was a conversion of a segment of the Half-Life campaign which involved navigating past several Sniper nests. No such official content has been made for Team Fortress 2, though one map shares a name with the original Half-Life Death match map, but has otherwise nothing in common.