Whilst you can't truly separate one 'type' of Judo from another and to do so would be a vast oversimplification as most if not all separations are, and I agree that such separation would serve little, I find the term highly multiaccentual and do not think that you can realistically say that Judo is Judo is unequivocally Kodokan Judo.
Of course, you could argue that whilst there are multiple interpretations of what Judo may or may not be, 'Judo' refers to a very specific concept and set of practices, and the rest are merely adaptions, variations, or simply misnomers. But people and society are and is dynamic and complex and once an idea takes any form external to its creator it takes on an existence of its own, if you will, equally if not more dynamic and beyond the conceptions and intentions of the person that conceived it. This applies to art, to literature, to music, to language, to religion and so on; if it can be interpreted then people will interpret it and they will do so in a wide variety of ways.
My point is that there are differences, sometimes minor, sometimes less so, and I think that to ignore these differences would be just as much of a mistake as it would be to turn them into absolutes.