From what I understand F1...F4 correspond to the 1st...4th resonant frequencies of speech. Why do we not just call them resonant frequencies? Or, in physics, why don't they call resonant frequencies formants? What distinguishes formants from resonant frequencies?

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Formant is a term used in speech research, and was coined 125 years ago by Ludimar Hermann (see this account), whereas resonance in the field of physics dates back to Pythagoras (the Latin term is a sufficiently ancient term that its hard to say how long ago the concept was given that name). The reason why other sciences don't use our term is that they got there first. Plus, they refer to different things.

Resonance is the tendency of a physical system to oscillate at great amplitude at certain frequencies – it's a property of the thing. A formant is an acoustic analytic product, the peaks of a sound spectrum. The former causes the latter. In Acoustic Theory of Speech Production, Fant says 'Conceptually these should be held apart but in most instances resonance frequency and formant frequency may be used synonymously'. See this article for discussion of the more variable terminology in speech research.

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