The resume is used to apply for a specific job and doesn’t typically extend past one page. The curriculum vitae (or CV) is far longer and acts as a longer record of all your academic credentials. The actual length of a CV will depend on your level of experience and the number of publications under your belt. Unlike a resume, the CV always starts with the education section.
Typically, CVs are used to apply for fellowships, grants, post-doctoral positions and teaching positions in high-level academic settings, such as universities. Some graduate schools can also use CVs, but for the most part, will only require a resume with a publications section.
Outside of the academic sphere, CVs might not be the best option to use unless otherwise requested on the job posting. In any case, you should always check the job or course description to make sure that you use the right form.