Street photography is a frame of reference. I agree with whomever said, if there is any clear-cut definition at all, it is highly subjective.
Aviotus' shot of the little girl that popped out from around the corner... is a great example. Beniliam's work in our Forum is superb. I'm including my own shot of a very pretty young lady on a Jerusalem, bus done my first time out with a Kiev; I got a lot of comments on this one.
Often in street photography, you make non-verbal contact with the subject via body language. In an instant, something "clicks." THEN, you click the shutter.
Cheers, mike