I’m not a fabric coloring expert. My MIL worked with hand-coloring fabric for a good part of her career, but she is in hospital so I can’t ask her right now :(. Anyway, my understanding is that faded black refers to the process of taking a black piece of fabric and bleaching it slightly, traditionally with sunlight, but I think that I am correctly remembering that nowadays a bleach effect it can be done in all manner of ways, like with lasers and ozone. So faded black looks like it has highlights and lowlights depending upon where the light hit the garment over time.
In contrast, a dark heathered gray is traditionally made by subjecting only some fibers of a yarn to the blackest dye and reserving some fibers to spend less time in the dye vat, before weaving the fabric, so that there are subtle variations in color.
However, nowadays they also make heathered gray polar fleece, which I think is essentially synthetic fibers which I think are first woven and then felted by mechanical means. In that case entire thin threads are probably extruded in various shades of gray or black. Anyway, the point is that in heathered gray the highlight and lowlight shades are densely packed together, and the net effect is a bit like sunlight reflecting on a pond on a breezy day.
In practice, I think retailers refer to “faded black” or “near black” when the black is less saturated, because of either less dye applied from the beginning (so that the raw material color comes through more) or because of something which has been made to appear bleached. “Charcoal” can be heathered, thread or can have a bit of white mixed into the black dye before the garment is knit or woven, or in the case of leather before the hide is tanned. I think being able to add white to things being dyed is a fairly recent development in the history of textiles, because dyed white non-plastic things mostly come from being colored with white clay and white clay isn’t very effective by itself as working as a dye.