TLDR: it seems that they originated separately but underwent convergent evolution over time (“Parthian shot” originally contained a strong additional sense of “fighting dishonestly”). Modern OED scholars seem to think that the modern use of “parting shot” is at least influenced by “Parthian shot”.
Is this where the term “parting shot” originates from?
https://english.stackexchange.com/questions/15416/parting-shot-origin#15440
TLDR: it seems that they originated separately but underwent convergent evolution over time (“Parthian shot” originally contained a strong additional sense of “fighting dishonestly”). Modern OED scholars seem to think that the modern use of “parting shot” is at least influenced by “Parthian shot”.