Is black a shade or a color?

Aha a good old question. By rough definition:
Colors is the particular wavelength of light
Shade is how light or dark that color is.

Real Black. Real honest to goodness strict-definition Black is a Color.
It is a wavelength of "null". It is the color your eyes see when your eyes don't work. Just as real White is a wavelength of "all-of-em".

BUT it becomes a problem when you try to put it in practice. There is no such thing as a True Black object, it will always be a little off. Have you ever tried to match black clothes? Same problem, unless they come from the same batch of dye they are always a little different. In that sense, black is a shade
We can't create anything that is perfectly black or perfectly white, we can mix up Colors and wavelengths to get pretty close but what we eventually end up with is always a Shade. So if you're talking about that tube of black paint in your hand, that is a shade.

trivia note - the most perfectly Black object on Earth (that I can think of) is the eyeball. Under the layer of white, and the colorfull iris, your entire eyeball is covered in a thin layer of black material. This material is only visible in your pupils. It's so Black that all wavelengths of light that humans are able to perceive can be absorbed and pass right through it.