In Season 2, Episode 6 of Terminator: The Sarah Connor Chronicles, Cameron fights a red-headed female Terminator.
When both machines reach for the same door, each realizes who the other is and they begin fighting in the elevator. When humans are about to enter, they stop fighting and face away so the humans won't notice the damage they've sustained. After the humans leave, they resume fighting.
This is normal for Cameron, since she doesn't want to blow her cover - but what about the other terminator? Other terminators, Cromartie especially, don't care to fight in front of witnesses. Why does this particular terminator care about that?