For positions in academia, employers frequently want a "CV" in addition to a résumé. The difference between a curriculum vitae and a résumé is a distinct one:

• A résumé (usually one or two pages) is a tightly focused summary of personal, education and experience qualifications intended to demonstrate fitness for a particular position. A résumé promotes an individual's strongest qualifications, as they relate to the specific or general purpose for which the material is provided. (See Résumé Guide.)
• A curriculum vitae (generally three or more pages) is a comprehensive biographical statement emphasizing academic and professional qualifications and activities.

Unless specifically requested, it is usually unwise to send a CV for a first contact. It is far better to start out with a one- or two-page résumé than it is to stifle the reader's interest by prematurely sending an overly long CV. You can always include a notation on your résumé that a CV (and/or references) can be sent upon request.