fur color in cats is x-linked. The specific color can be darker or lighter in individual follicles (causing stripes) or the color in the follicle can be "turned off," causing the follicle to produce white hair, but two completely separate colors such as black and orange have to be coded for by two separate x-genes. So, all "calico" cats (orange, black, and white) are either female, or have some rare intersex genetic mutation where they still have two x-genes (XXY, XXYY, etc).

The Calico coat pattern has a number of variations / subtypes that this still applies to. One is something called a tortishell, which is a calico that just doesn't have a lot of those "turned off" white patches. There's probably some specific % in cat breeding circles but the core concept is just "two separate colors that aren't white but also no or very little white," (again, white doesn't count as one of the x-linked colors because it's just a "turned off" follicle). Another variation is a "dilute calico" where instead of black and orange they have a sort of faded / pastel version of the two different nonwhite colors (grey and cream). The pictured cat appears to be a combination of the two, or a "dilute tortishell" where she has the two separate colors, grey and cream, and not a whole lot of white.

So basically I can say for certain that that cat has at least two x-genes. Whether or not it also has one or more Y-genes, or three or more x-genes isn't impossible, but it's pretty unlikely. I guess technically "mutation" isn't quite the right word ("variation" maybe?) but the exact right term escapes me for the moment.