Apart from the fact that resumes are more commonly used in America that in Europe or the UK there is not much real difference.
Both documents have the same objective which is to help jobseekers gain a interview with a employer. They intend to give recruiters an accurate description of a candidates employment history and skill sets.
A resume is considered a shorter version of CV’s, giving a more concise targeted list of relevant transferable skills and accomplishments. It is usually only one page long as you do not have to list your hobbies or personal interests etc.
A CV tends to be longer than a resume and contains much more detailed information about a candidate. Although they should be no longer than two pages long, many CV’s stretch to five or six pages. They tend to include extra information like details of any successful presentations, awards or membership of professional bodies.
If you are applying for academic jobs then it doesn’t matter if you are in the USA or Europe you should use a CV format rather than a resume.