Black Smoke or Smoke Tabby Cat?

I know very little about genetics, the mode of inheritance of colours etc in cats; but having Isla means I have just had to look it up and find out what I can about Smoke coloured cats. Though I guess most of the information applies to pedigree cats I'm still curious and have lots to learn.
A page on common cat colours makes no reference to "Smoke Tabby's"  .....
"If your cat is pretty much solid black or gray, but the roots of the hairs are distinctly white, it is a "smoke." (It's normal for the roots on a solid cat to be grayish; true smokes, on the other hand, have definite white roots.) Smokes are the solid version of silver tabbies. These cats are very dramatic because when they move, the hair parts and the white undercoat can be seen.

• A "black smoke" is a solid black cat with white roots.
• A "blue smoke" is a solid blue (gray) cat with white roots."

It seems one parent has to have a white undercoat for the kitten to be a smoke. It is Often difficult to tell them from solid colour kittens except that smokes sometimes have white around the eyes and a paler stomach. It may take some months to tell which kittens will be smoke because the full coat colour is sometimes not seen until the adult coat comes in at 2 years. Undercoat begins to show at 3 weeks, and by 6-8 weeks they have a mottled look.
"The bottom eighth of each hair is white or creamy-white, with the rest of the hair being a solid colour. Genetically this colour is a non-agouti cat with the dominant inhibitor gene; a non-agouti version of the silver tabby. Smoke cats will look solid coloured until they move, when the white undercoat becomes apparent. It is mostly found in pedigreed cats (especially longhair breeds) but also present in some domestic longhaired cats."
So it seems "Black Smoke Tabby" is colour/coat pattern so it has NO bearing on personality or anything else and there's no "history" on it. "Smoke" is simply a colouration where the hairs are white at the base and black at the tips. And tabby as we know is a coat pattern. So little Isla is a Black Smoke Tabby ..... I think!!!!! (or a Black Smoke ... or a Smoke Tabby ... lol)