Difference between "résumé" and "CV"
Solution 1:
In modern English and in the HR sense, they are pretty much used interchangeably and most people assume they mean the same thing.
If you look at their etymology, though, "curriculum vitae" should technically describe what happened over the course of your life, i.e. who your parents were, when and where you were born, upbringing, education, etc., before going into your work experience, while "resume" should sum up your relevant experience and is arguably targeted to your audience, i.e. if it's for an IT job, you'd leave out that you worked as a waiter during your Uni years and you wouldn't think of mentioning your parents (unless maybe their names are Bill Gates or something).
So I would always call what I send for a job application a "resume", but recruiters in my space (IT) typically say "please attach your CV" and mean the same thing. I suppose which you use depends on how pedantic you want to be....
Solution 2:
A simple difference:
CV is WAY LONGER.
Resumes come in a million forms, but they are almost always concise and one page long.
CVs, however, can run on for an untold number of pages-- they usually represent a PhD-holder with a very extensive list of publications, research contributions, and work experience which they wish to share. I've seen CVs go on for a dozen pages.
So in essence, a CV is a bigger, badder resume. 90%+ of people don't need one, and employers don't want to see one.
EDIT: This is only true in the United States. The terms have different meanings in other countries.
Solution 3:
In my experience, the CV Curriculum Vitae is used more in Britain and is quite thorough, 2/3 pages in length. Whereas a resume is usually a single page, used primarily in the US.
Now, as I said. That's my experience of it having successfully applying for jobs in both places - Others' opinions may differ.