Not to be picky, but "resume" is properly spelled "résumé." You may see "résumé" spelled "resumé" or "resume," neither of which are quite correct and the latter of which can be confused with the verb "resume."

But to answer your question – résumé is a French word meaning "summarized" and CV – in full, curriculum vitae – is a Latin term meaning "course of one's life." Therein lies the distinction: while both documents contain the details of one's education and work experience, a CV is a long, detailed version of a résumé. Most people only ever need a résumé – a one- to two-page document detailing her/his contact details, education/certification, and experience. A CV contains more detail – publications, abstracts, presentations, invited lectures, and media presentations – and is usually only used by doctors, academics, and administrators. But, in common usage, a résumé is the same thing as a CV.