I stopped short of hitting him.
Does it mean exactly the same as "I almost hit him"? What else does the expression convey?
It's hard to say. It could mean the person did other things (yelled at him, verbally intimidated him, maybe even pushed him), but did not physically strike him with force. Or it could mean the person did nothing to him at all, but he was tempted to, to, and almost got to the point where he would, hit him.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.