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well if you do the "Square" you've got EE AA, EeAA, eeAA, EEAa, EeAa, eeAa, eeAA, eeAa, eeaa, EEAt, EeAt, eeAt, EEat, Eeat, eeat, EEtt,Eett, eett. Some would say EE and Ee are both black ; but i do know a lot of breeders in the "real" world advertise for "HOM Black" or "Het Black" so while visually it might be the same base coat, technically and genetically they are different. In this case my answer would be 18. I think it really depends on how you are breeding; is the goal HOM what ever or is the goal Het whatever?

Horses have two pigment types, red pigment, and black pigment. E horses make black and red pigment and ee horses make effectively only red pigment. That is my dividing line. Black and bay are just different variations of the black-and-red base type.

ETA: Chinchilla probably qualifies as a unique base as well as those horses are black-only but as a fantasy gene I don't count it.

https://www.animalgenetics.us/Equine/Coat_Color/Red_Black_Factor.asp

To be clear all horses have both kinds of pigment. The extension gene does not control if a horse makes black or red pigment. Instead, it controls the Melanocyte-Stimulating Hormone Receptor and that receptor controls the ratio of the pigments and helps regulate the amount produced. That animal genetics site above and many many websites incorrectly treat extension as a switch that toggles a horse between all black or all read and this is simply untrue.

Dominate extension horses tends towards the black pigment side but still make lots of red pigment. Agouti controls the pattern this shows up in on the horse. Recessive extension horses are predominantly red pigment as agouti does not act on red pigment we don't see any noticeable effects from it on ee horses. It is still doing stuff, just not in a way we can spot.

It's one of those things where the more you drill down the more layers of "well actually it REALLY does..." you get. "E switches between red and black" is good enough for the vast majority of discussions.