Do you mean "closely related keys"? These are keys that share most of the same notes and are generally one accidental away from each other. Visually, if you're familiar with it, these keys are next to each other on the circle of fifths.
F major and C major are closely related because they are next to each other on the circle of fifths and are only one accidental apart (C is a perfect fifth above F).
So generally, F minor would not be closely related to C major. C maj has no accidentals, and F minor has 4 flats. Conversely, as you say, C min and F maj are also not closely related. C min has three flats and F maj only one.
I hope this answers your question!