All cats are genetically tabby. Solid coloured cats have a gene which causes the dark pigment (black, brown etc) cells to stick in the 'on' position, rather than switch on and off which causes the dark and light banding on the background hairs (agouti) in tabby cats. In effect a black cat (or a blue, chocolate, etc) is a tabby cat with the light background areas filled in using the same colour that would make the stripes/spots/blotches.
In some solid coloured cats you can see faint tabby markings, these are called ghost tabby markings and are caused by the red/yellow pigment component of the underlying tabby pattern showing through the black mostly at the roots of the hairs where the black pigment is less dense. Solid kittens often have ghost tabby markings but grow out of them as they get their adult coat, this is because kittens produce less dense dark pigment than adults.