Yes, you are right, people can kill someone when enraged. And maybe in some cases could attack severely without intending to actually murder but somehow they hit too hard, for example, and do end up killing them. But I believe that for a lot of them they actually do mean it, in the moment they do actually want to eliminate the person. Hard to understand if you are not that type of person, but what I'm saying is that just because they want to kill someone and only get that desire in a few minutes or so, doesnt mean they dont want to kill them.
Also, it just occurred to me in trying to explain this, and also sparked a bit by what you said heloise, that it could be that the real 'accident' in many cases of severe domestic violence is that you don't get killed? Meaning that the attacker really did want to kill you but didnt go far enough to actually do it - more of a fluke it didnt happen? (I'm not saying in your case, but just that it made me think).
I understand it's hard to accept that there are murderers, therefore hard to accept the way their minds work. I think perhaps because of the whole confronting and frightening nature of murder, and what a murderer is, that people try to put a positive, less horrible spin on it and the murderers nature and intent.