There was a time when a knitter could simply talk about the "colours" of yarn. ("I'm making a yellow hat for my daughter, and a pair of green socks for my son.") Though the final knitted product might have multiple colours in it, thanks to striping or thrumming or more elaborate techniques, each individual yarn that was used for the project would generally be just one colour.
These days, however, variegated yarns are popular. In many cases, it doesn't make any sense to call such a yarn simply "Red," since there might be a dozen jewel tones reflected in the yarn -- scarlet with shades of plum and burgundy, perhaps. That sort of yarn might be labelled as a red colourway, which is knitters' code for saying it's "red, but not just red." (Even more likely, the yarn manufacturer might come up with some evocative name for it like "In the Court of the Crimson King.")
Sometimes, the colours within a colourway won't even be related. Koigu is one yarn manufacturer that's famous for including half a dozen (often clashing) colours within a single skein. Knitters tend to name these colourways "conceptually": "I've decided to use this sunset on the beach colourway for a scarf I'm making" might be a way of referring to a yarn consisting of blues, greys, and oranges.
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