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In short, is there a relation between the preposition cum and the conjunction cum?

It makes some sense that the conjunction would come from the preposition. One could interpret some cum clauses so that the main clause happens with a condition expressed in a subordinate clause or at the same time with the subordinate clause. Perhaps some other kinds of connections would make sense, too.

I have seen both cums discussed in many places, but I have never seen any comparison between them. Is the similarity a coincidence or not?

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    I've read that the two senses of cum converged from two unrelated Proto-Indo-European roots, the conjunction being a frozen accusative relative/interrogative pronoun and spelled quom in Old Latin; its feminine sibling is quam. Hopefully this comment provides from useful search terms for someone who wants to dig deeper. This looks like a good start. – Ben Kovitz Jul 12 '16 at 16:29
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    I'm wondering how many people came through HNQ not realising this is a question about latin. – John Dvorak Jul 12 '16 at 19:19
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    @JanDvorak, I know the title is easy to misunderstand, but I chose it because it asks my question concisely. And if that HNQ listing brings more people to the site for whatever reason, I'm happy. The end justifies the means, I guess. – Joonas Ilmavirta Jul 12 '16 at 19:28
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    @JoonasIlmavirta: Indeed, what counts is a happy ending. – Cerberus Jul 12 '16 at 20:15
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The similarity is a coincidence; these words are unrelated. Etymological dictionaries such as De Vaan's give the following account of the two words:

The earlier form of the conjunction cum is quom; this is attested in early Latin, and also in the word quoniam (< quom iam). It is descended from Proto-Indo-European *kʷom "when" and has cognates in other IE languages, including English when.

The earlier form of the preposition cum is com, which remains its form in compounds (com-). This is from PIE ḱom "with", which also has reflexes in other languages, including the Germanic verbal prefix ge-.

The Italic cognates suffice to show that the first sound of the conjunction was a labiovelar (Umbrian pumpe "whenever", with p from ) but the first sound of the preposition was a velar (Umbrian kum-).

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