There is a number of resume types. Most people use a chronological resume, which presents your experience in a reverse chronological order. This is the preferred format with employers.
A functional resume groups accomplishments using skill categories (e.g.., management experience, communications experience, technical expertise, etc) rather than using separate job entries. However, some people use functional resumes to hide gaps, which is why functional resumes tend to be viewed with suspicion. One way to address that is to use a combination of chronological and functional—showing skill categories but also including a brief work history—rather than just a functional approach. This type of resume is typically used in career transitions to emphasize transferable skills. Employer information also is included after the skill areas and accomplishments are enumerated. As with all resumes, bulk the most important information toward the top of the resume when choosing a functional format.
A curriculum vitae is a document that comprises all of your professionally-related activities. It can be any length. Many international organizations accept a CV. Specific fields, such as academia, require a CV.