A Curriculum Vitae is usually reserved for only a select few opportunities. Among them are international jobs, fellowships, grants, research, scientific and academic positions. A complete Curriculum Vitae will include more detailed information than you might include in a resume. You’ll likely want to include complete and detailed information about education and research that you have completed. Presenting a complete image of your capacities that qualify you for the opportunity!
A cover letter should include the most general of you. It might include things like your name, contact information, brief information about your education, research, and/or work experience and some description of your intention. It shouldn’t have as much information as a complete resume might, but it should compliment your Curriculum Vitae in a way similar to a mini-resume. Introduce yourself and what you have to offer and include the details of that in the Curriculum Vitae.
If it were the story of you, how would you begin? That’s your cover letter. Then use the Curriculum Vitae to provide the details.