That is the nut of the case. Zimmerman 'claims' he was jumped, was pinned to the ground, pummeled with punches with his head hitting concrete, and finally struggled for control of his firearm.
The prosecution contends that Zimmerman, armed with a gun, profiled, stalked, confronted, and shot Travon Martin.
In your 'cop scenario,' it's obviously self defense. In the first (I believe correct) Zimmerman scenario, it is obviously self defense.
In the second (prosecution) scenario, it is at least manslaughter.
I'm not seeing the lack of the same self-defense. Unless security watches and even public curiosity about unusual behavior is declared illegal or aggravating per se, there is nothing wrongful about being armed with a gun, profiling, stalking, and confronting someone where there is reasonable cause for these behaviors. As for the shooting itself, it doesn't even matter if those behaviors were wrongful, if they can't be used as a legal justification for St. Trayvon to physically attack Zimmerman. Once that attack takes place, Zimmerman is under no obligation to allow himself to be harmed or killed - none whatsoever. Thus self-defense trumps again.