There are 5 colors in Magic and many characters are associated with one or more of these colors. The colors thematically represent aspects, but are the characters aware of the existence of these aspects? For example, does Teferi know that he is a blue-white mage?
Characters know that forming mana-bonds with different areas (mountains, swamps, forests, etc.) will give mana that can then only be used for specific purposes; i.e. a mage who draws upon a mountain mana-bond will gain mana that can be used for creating fire, earthquakes, etc. whereas drawing on mana-bonds from the sea will give magic that allows for illusions, etc. Consider this 1999 story, where the mage Feldon visits various colours of wizard and learns from them. The scholar in the story says:
"Green calls to the living," he said. "Black calls to the dead. Blue creates the shadow of life. Red consumes, and that's very important as well, because you must often destroy before you can build. I study, and the magic I wield is White, which is the magic of comprehension and understanding."
Therefore yes, the in-universe characters (or at least some of them) are aware of the various colours of mana and what each is for.