Hardly two defining moments for Khan.I am not sure.
I am.
From little things like the fact that he familiarizes himself with every detail of his enemies' vessels so that he can overcome any defenses right up to the fact that when his victory is frustrated he always goes a little nuts and is willing to destroy his adversaries at the likely cost of his own life.
Leaving aside the ethnic origin (Sikh as said in space seed) there's also the fact that Khan was obviously a babe magnet. Plus the Khan from space seed was too proud to let himself hit in the face by Kirk without smashing his head. Add to that an endless list of minor details that together scream that this is a very different person.
The only babe Khan attracted in Space Seed was Marla and she's easily swayed.
I don't even recall any attempted head hitting in Space Seed. In STID he allowed it to show how ineffectual Kirk was. A very Khanlike move.
Khan is about barely concealed contempt and arrogance. Khan in STID had that in spades.