Koryu are the ancient Japanese martial arts that were actually practiced by the samuai. Modern Japanese martial arts just as karate-do, aikido, judo, and kendo are Gendai Budo. Gendai Budo is descended from Koryu. They have much in common, but they are really very, very different things. Koryu was meant to be handed down from generation to generation in a most exact way. If a given master instituted a variation from the canon, he would then create a new branch of the main system (-ha, Ono-ha Itto Ryu is a branch of the main Itto Ryu). Whereas in Gendai Budo, each master student seems to recreate the art. You can look to the profusion of aikido styles as an example.
A must-read if you're interested in the subject of ancient Koryu and modern Budo is the three volume classic by Donn Draeger: The Martial Arts and Ways of Japan.
Below is an excerpt from an article about Koryu. You can read the full article here.
Authenticity in Koryu
The whole issue of authenticity is one of those things I struggle with a lot, when I'm thinking about koryu.
Here's how a lot of people seem to think about koryu:
The best koryu have been passed down from generation to generation from the time of the samurai. The best warriors distilled their knowledge of practical fighting techniques and the skills necessary to survive a life-and-death struggle, and taught them faithfully to their students, who, through long and hard study, and deep insight into the techniques, mastered the techniques themselves and, in turn, passed them on unchanged to their students. And so on through the ages.
If that view is correct, then koryu represent not only a priceless cultural/anthropological heritage, but also an invaluable insight into effective combat techniques. Unlike modern "budo", these koryu "bujutsu", having been handed down from the time when life-and-death battles were a reality, must reflect true, killing techniques.
The model for transmission, according to koryu purists, would seem to be some kind of "photocopy" model. To use a visual analogy, the founding master creates a "map" of the techniques. Through diligent study, his chosen successor copies the master, creating an identical map, much like a photocopy of the original.
People who think this way believe, not only in the possibility of "true and correct transmission" but also in its likelihood. Consider this: Many currently-practiced koryu are on somewhere between their tenth and twentieth generation, and the current state of the art must reflect "the weakest link", so to speak, in that chain of ten or twenty masters. In other words, if there was even one "bad teacher" in that chain of teachers - someone whose understanding was less than complete, or whose physical mastery was less than perfect - then the subsequent generation would continue to propagate that error, or that weak point.
Koryu purists would argue that only the best students would be chosen to continue the school - those pupils who, through long and hard apprenticeship, would have the very best mix of understanding and physical mastery.
But isn't the reality far more complicated, and less ideal than all that?