Haha, I don't go around calling myself a street fighter in public. This conversation hardly comes up when I'm out in public, but I guess if I got called out, I'd have to resort to self defense if somebody wanted to 'test me'. But I don't walk around like a hardass, so it probably won't happen too often.
Sorry, but I'd have to say that your use of self defense, as you describe above, would fall into the fighting category, not SD. This is one of the main reasons why I don't like to discuss martial arts or my training with people, unless I'm sure they're sincere with their questions. When they start making the Bruce Lee sounds, well, whats the use? LOL! I enjoy my training and by all means, if someone wants to know something, ask, but again, when people start acting stupid or 'calling me out' by asking if I think I could kick their ***, if I could beat this person, etc, I tend to walk away, not take the bait and give in to their 'test' if thats what you wan to call it. LOL.
Just because someone is talking ****, doesnt mean you have to give in to it.