In say C minor, with its 3♭ key sig., there are the notes C D E♭ F G A♭ A♮ B♭ B♮ that can and are all used - they do not make up a single minor scale. We are aware of this when considering the minor key and scales associated. Scales and keys are directly related, but not synonymous. Although with just the Bb, it may not be F major, it could be D minor - or even C Mixolydian! They also tell us, indirectly, what the key is likely to be. for each major key, and they're usually stated at the beginning of each line to remind us of what they are, to save using accidentals instead. It just happens that diatonically, all those notes (C D E F G A Bb) are also those from F major. The root is C, but the notes are not from C major, or C minor (any of them!) but C Mixolydian. So, in, say, C Mixolydian, that's what we're in. The reason for mentioning any letter name is to tell what the root, or 'home' is. It would be F major rather than F minor, as there's an A in C Mixolydian, not A♭.
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