I believe the term "Hot Rod" began in the 1920's when anything that was beyond the normal was "hot", such as "Hot Jazz"or a "Hot Chick" (which is short for chickadee). Since almost all cars were Roadsters then, one that was modified was a "hot roadster", which was probably shortened to "Hot Rod". That term became a symbol of lawlessness and bad behavior (like jazz). So as was stated above, the term "Street Rod "was born in an attempt to get away from the negative images of young crazy's tearing up the road for thrill's.
Also.. If your Hot Rod is street legal I guess it's a street Rod.