Having now checked the OED, I find there is no difference. The zoo- forms in each case (-morph, -morphic, -morphism) precede the therio- forms by a few years or decades, but the quotations don't illustrate any difference. Neither mentions the other, but both are contrasted with anthropomorphism.

When I first posted theriomorphism it was because I had recently read about it and had the impression it was the form used in discussion of Egyptian religion. (The person using the word was an expert graduate student, but a philologist rather than specifically an Egyptologist.)