what is the difference between the prefixes 'quad' and 'tetra', 'penta &quint' tri/tert

English language borrows from many eclectic sources. Greek and Latin provide different words with similar meanings. Check the etymology in any good dictionary.

Greer Evelyn Jeremiah Kellan Taylor Aurora Bennett Ciaran Mya Noelle Serenitie Anastasia

We have both forms in English because words came into the English language from different sources, and the prefixes often came with them. There is no rule, other than common usage. Be glad you aren't studying Swahili. That language is made up of five roots and conjugating verbs depends on which language base that verb uses, and each of the five is different. Now that's a challenge!

latin vs greek... not sure if there is a rule that governs when one is used over another.

If you have to ask then you need some real help.haha just playing I could not even give you a guess. Good luck!