Literally Curriculum Vitae mean "The course of life" and Resume means "Summary". The major difference between them is their length. While considering both, CV is a detailed one that includes the information about your educational, academic details, teaching experience, research experience, publications, presentations, awards, honors and other details.
But, a Resume is to the point and it strictly consists of the information that is relevant to the job. Potential employer needs only the resume and not the CV. Mostly the CV may consist of more than two pages but the resume can be expected of less than two pages.
In both CV and resume you should include your full name, address, contact information, education work experience and skills. Don't add irrelevant information to your resume and don't miss out the essential things in your CV. List your work experience in reverse chronological order. This format is not only easier for people to understand and is also considered professional.
In America, the general rule is to use a resume. But in some of the countries a CV is expected and often they are demanded. Most of the companies don't like lengthy descriptions and prefer the concise ones. Each word in your resume must have some worth or else it should be avoided.
Moreover, while applying for two different jobs your CV could be the same but your resume has to be different and specific to the job you have applied for. The different achievements that you have made related to that particular field should be highlighted in the resume. This shows that you are an eligible candidate and makes your resume stand out from the others.