For example, take red --> it can be lightened by mixing white and then it would be pink, but still a shade of red; it can be darkened with black and then it will be dark-red colour but still can be considered a shade of red.

Same thing with blue: light-blue (sky-blue / baby-blue / whatever you want to call it) and dark blue (or navy blue, etc.) but it's still a shade of blue.

Ditto for yellow, green, violet, orange, and almost any colour.

But what about white? And black?

Would you say grey colour is their shade?

I've seen once on a can of paint labelled "Porcelain White" and "Cloud White", I can't quite picture how such colours will look like.

Of course, there are different tones and shades of white, grey, and even black.

Black and white are not colors. Think of white as a blinding light, and black as a deep shadow. They are used to make colors pastel (adding white) or dimmed (adding black). If you see a "bone white," or a "cream," an "ash grey," "blue black," etc., those are not variations of black and white. Those are colors- oranges, pinks, blues, etc., that have had black and white added into them. A cloud white might be a little cooler than a flesh white, for example, and that is because it is a fraction of blue mixed with a large proportion of white. It is still the blue that is making the pigment, though, never the white.
B&W are what accent other colors.