Interesting.
According to the Oxford and Longman dictionaries I looked up, "tabby" is definded in terms of its fur. However, the "Longman Lexicon of Contemporay English" quotes the masculine of "cat" as "tabby". The "Collins English Dictionary" uses the above mentioned description on the first definitions of the word as an adjective, but as a noun, the first definition is "a tabby cat" and the second one is "any female domestic cat".
The Merriam-Webster Dictionary defines "tabby" as "striped or mottled domestic cat; also: a female cat".
I'm "pussled"