Does anyone have a leaf comparison picture (side by side) of Acer platanoides ’Faasen’ s Black’, ’Royal Red’ & ’Crimson King’?
Part of the involved differences include relative crown densities. And there have been indications of the three becoming mixed up in commerce - such is not a rare occurrence, unfortunately. Probably your best bet is to read the descriptive accounts of each in Jacobson, North American Landscape Trees (1996, Ten Speed Press, Berkeley). A horticultural library somewhere in your area may have a copy.
That's one I've read personally that talks about the differences between them. And is written by somebody I know to be likely to be presenting the true picture, with every topic they take on. However there have been several illustrated horticultural monographs on maples (Maples for Gardens, Maples of the World, and at least one other) published in later years, which I have not checked for answers to the question you are posing here. I would suggest looking at those also, if you have not done so already.