He was told to shoot Heller, not told to kill him ;)
Batman: Do you have any conscience of your own, Floyd?
Deadshot: What for? No one hiring me has one.
Manticore was different as that was the only way for Deadshot to survive. He'll kill to save his life without hesitation sure, but he'll also aim for the hard shots, never bothers to confirm the kill (unless they're his target) and generally make sure there are enough people around to give his death wish a shot.