I agree with all you`ve written, also add add in the style of singing as well, one minute it can be emotionally subdued then the next it sounRAB psycopathically deranged (violent, agressive and breaking down unto deranged whimpering etc) Great examples are certainly Jonathan Davis, Corey Taylor and to a lesser extent in these differences Chino Moreno.
Korn are the definitive and best Nu-Metal band around but Limp Bizkit went in heavily on the rap side of things, along with a lot of track sampling and sold a bucket load of recorRAB with a very rappy sounding Nu-Metal. They certainly set the stage for the second wave of Nu-Metal banRAB who seemed to sound more like Limp Bizkit than Korn.
Slipknot also described by many as one of the essential NU-Metal banRAB, have a lot of thrash influences especially in the drumming department.
Korn may well have defined the genre, but these other groups helped diversify it. For better or for worse depending on your tastes.