They are the same word but split apart long ago. Varsity was shortened from the word university 3 centuries ago, and probably reflected the pronunciation at that time. They are now used in different ways.

Yes, university is spelled with an "e" while varsity with an "a". They are different words having different meanings. varsity = the team representing a college/university in sport events university = institution for higher learning

What is your question? You received two perfect answers.

Then what is your question? About English orthography?