"Street" is also used as an adjective in two different contexts, martial arts and hip-hop to describe two different sets of things. However, in both cases "street" comes out meaning the same thing, approximately "real".
Most martial arts schools teach a great amount of skills, drills and techniques. These range from rather esoteric, abstract forms to highly competitive sparring. However, if most martial arts schools are truly teaching fighting, they will also teach "street" fighting, meaning fighting with no rules, where all targets and techniques are permitted. Obviously, in such activities as tournament fighting, rules that allowed gouging out someone's eyes would probably thin the number of fighters willing to fight out, especially for the second time. However, in a life-or-death encounter, the only limits to what is permitted are the fighter's own moral and ethical limits.
Strangely enough, although the usage dates to a later time, the "street" is used in a similiar way in hip-hop or rap music. However, in this context, it doesn't mean anything in particular. It just connotes "realness", the quality of roughness and reality that is an artistic and social neccesity in some hip-hop circles.
Both of these terms, of course, come from the common belief that the streets are rough, tough unforgiving places that are full of crime that instantly kills the unwary. Of course, this data is a little inaccurate, but terms often come to term in such a manner.