[thaumasiotes]

Homographs are words that are written identically. I don't understand what you're trying to ask - the etymology of a word is not at all relevant to how it's spelled.

[empath75]

it's relevant to whether it's a homograph

[thaumasiotes]

No, it isn't. The spelling, and only the spelling, determines whether it's a homograph, because that's what "homograph" means.

Etymology is relevant to whether two words are cognates.

[empath75]

If the multiple meanings are merely variations on the same etymology, it’s not a homograph, it’s just a word with multiple meanings.