I'm answering from a United States usage perspective. A curriculum vitae is more often used in academic settings, or workplaces where people have advanced degrees and so are used to using that term from academia.
"Vita" I would understand as a shorthand for "curriculum vitae" but I can't say I have encountered it before; the preferred shorthand here is "CV". CV is probably used more often than the full "curriculum vitae" term in the US.
"Résumé" (often the accents are dropped in the US, to "resume", or only the final accent is there, "resumé" -- all three are listed as legitimate spellings in the American Heritage Dictionary) is more a business term. Resume tends to be more common than CV, and would be the term I would choose as a default if you don't have an advanced degree or aren't applying someplace with an academic flavor.
"Maintenance History" sounds to me like something for an automobile -- I've never heard of it being applied to a person's work history. UK English, perhaps?