I don't think this is really a bad question - food terms can be the sort of words that can travel readily between languages (Wanderwörter). Consider ketchup, sugar, ginger, tea.
In this case, though, the relation between L garum and May garam does seem to be a coincidence. Or at least, there is no recognized etymology which connects them that I can find.
Anecdotally, I will note that there is another word which is nearly homonymous with the others, and which also refers to a type of seasoning: Hindi गरम garam, which means "hot" and is often used in the sense of "spicy" (e.g. the popular spice blend garam masala). But this garam is said to derive < PIE *gʷʰer-, so it's likely yet another coincidence.