Tabby refers to the pattern on a cat's coat and is not a breed. The name "tabby" is believed to have derived from Atabi, which is a type of striped taffeta (known as tabbi) that was manufactured in the Attabiah district of Baghdad.
The word tabby was derived from a kind of taffeta, or ribbed silk, which when calendered or what is now termed "watered", is by that process covered with wavy lines. This stuff, in bygone times was often called "tabby:" hence the cat with lines or markings on its fur was called a "tabby" cat. But it might also, one would suppose, with as much justice, be called a taffey cat, unless the calendering of "taffey" caused it to become "tabby". Certain it is that the word tabby only referred to the marking or stripes, not to the absolute colour.
Genetically all cats are tabby, however many possess "modifier" genes which inhibit this pattern from being expressed. The mackerel tabby (Mc) is the "default" (wild type) pattern, with the classic pattern being recessive (mc). Recessive genes require two copies (one from each parent) in order to be expressed. The spotted tabby is essentially a mackerel tabby with a modifier gene which breaks up the markings from stripes into spots. If cats were allowed to do their thing (so to speak), and no more selective breeding occurred, then they would eventually revert back to the default tabby pattern after a few generations. This is known as "revert to type".