I recently attended a "preparing for the job market" workshop for PhD students where the speaker instructed us in no uncertain terms that we should always refer to a "curriculum vitae" and never a "curriculum vita." Following the workshop, I made sure to replace all instances of "vita" with "vitae" on my website.
Today, though, the professor of a class I'm taking asked me why I had the word "Vitae" (on its own, without "Curriculum") on the menu of my website, suggesting that "Vita" might be more appropriate. I looked around this website to try to get some clarification and noticed not only that there didn't seem to be anything on this topic but also that some people use both spellings in the same sentence (e.g., "A 'vita' is just a short term for a curriculum vitae").
So, is it "vitae"? "Vita"? "Vita" when the word is on its own but "vitae" when it's "curriculum vitae"? Also, is there any reason (based in Latin or something else) for these distinctions?