Well, a hacker being someone who hacks makes sense, but just because you have hacked, doesn't mean you do hack, so you're right, having hacked doesn't really make you a hacker.
I believe there is a correct definition of what a hacker is, though mine may not be exactly right, I'm fairly confident I'm pretty close.
"who cares what hacker means."
Generally, hackers care what it means, because people usually get it wrong, thinking hacking is about breaking the law and hacking people's computers illegally, etc.

If you'd like to read what I think a hacker is and what hacking is about, here's a link:
http://www.hackingdynasty.com/site/texts.php?sect=hacking&id=14