I feel confident enough to state that there can only be one reason why domestic cats have different coat colours and types. I put forward my thoughts on this page.
Orignal domestic cats were brown tabbies
We know that the original domestic cats were all brown, spotted tabbies because the original domestic cats were socialised North African wildcats. This was between 10,000 and 14,500 years ago in the Eastern Mediterranean. Over the intervening years to the present, initially hundreds and then thousands and now many millions of domestic cats lived with people. The ancient Egyptian paintings show pet tabby cats.
Genetic mutations and possible human intervention
We know that genetic mutations take place spontaneously (examples: Manx, Scottish Fold and Sphynx). It is as if a small error occurs in the copying process of the genes when new kittens are created. Sometime in the early stages of the domestic cats, let’s say about 8,000 years ago, perhaps (I am speculating) one of the spotted tabby domestic cats looked different. Let’s say a bit of white fur occurred and people liked the appearance. So even in those days, someone had the idea of breeding more these desirable tabby and white cats. Perhaps they sold some. Made a few shekels.
Over the next thousands of years there were more genetic mutations creating slightly different coats. Perhaps a pure white cat was born. Once again someone bred more of them informally. And then a white and black cat was unexpectedly born in a litter of tabby cats.
Domestic cats don’t need camouflage
Let’s also remind ourselves that the reason for the evolution of the spotted tabby coat of the African wildcat was to protect the cat as it provides camouflage. Domestic cats don’t need camouflage as they are not reliant on hunting for their food as it is supplied by humans. This allowed genetic mutations which created coats that were poor camouflage to become fixed. So even if people did not intervene and breed novel looking cats they would have bred themselves and survived.
Whereas in the wild genetic mutations which would have undermined the protection that the spotted tabby coat provided faded away because these cats would have found it harder to survive. Natural selection would have weeded them out. Natural selection does not work in the artificial environment of the world of domestic cats.
Gradual increase in coat colors and patterns
Gradually through a combination of (1) natural, spontaneous genetic mutation and (2) expansion of these mutations by humans selectively breeding from the mutated cats, we have ended up with a huge range of coat types and patterns.
Whereas until around the middle of the 1800s cat breeding was informal, since the late 1800s, cat breeding has been formalised and controlled to a certain extent which has further expanded the range of cat coat types and colours in pedigree, purebred cats.
In short the answer is about domestic cat evolution over thousands of years supported by human intervention.