I'm sorry if this is a super basic question, but could you explain how a black-based tabby ends up with either a brown or grey coat? I know we often call them brown tabbies or grey tabbies (when they have black stripes), but my understanding is that's technically wrong, and that they're black tabbies with 'x' color? Can you clarify?
It's not wrong, many registries actually call black-based cats brown tabbies, i just prefer black because it's more genetically precise. When someone calls a cat gray tabby, you can't really know if they're thinking grayish black or blue, and with brown, there is chocolate and cinnamon to consider.
The brownness/grayness of a black tabby is called rufous. This is basically about how strong the pheomelanin is in the agouti hairs of the tabby background. Stronger pheomelanin adds warm shades, makes the cat brown, weaker pheomelanin will result in a cold-toned, gray cat.
In this paper about bengals, they made a great rufous scale:











