Here's a quick, gross oversimplification: Judo = jiu jitsu minus the parts that leave you with no one to spar with.
Once upon a time, the story goes, the local hard guys could practice on the local peasants all they wanted, and when they broke a guy's neck they'd just move on to the next one. Times change and that sort of casual experimentation falls out of favor. The founder of judo, Jigoro Kano, realized that jiu-jitsu was doomed unless it could be made into an art or sport, something that could be practiced without killing or crippling half the particpants at every lesson.
My first judo teacher (Korean guy. Another gross oversimplification: Korean = Japanese + American sense of humor) had no qualms about showing us how to take the techniques a little further to make them as "practical" as necessary.
In the dojo you pull the throw so your partner can keep playing.
On the street you'd do the opposite -- follow him all the way down
and through. Add concrete instead of a mat, you're looking for the back of someone's head to become three inches closer to the front of his head. That'll "get her done."
Same instructor also said "You want to put a fancy wristlock on some guy with a knife? Hit him with a chair first, knock him out.
Then play around with wrist, impress your girlfriend."
When was the last time your instructor came at you swinging a chair?
