The most common resume format is called "chronological." It's simply a resume that lists your education and experience in reverse chronological order - most recent items first - and it's a good way to start a draft of your resume. You may also hear the terms "functional" or "creative" used to describe resumes. These are just variations on the chronological format that use headings that best showcase your background and qualifications.
A skills resume combines the skills you have from a variety of experiences - paid work, volunteer work, student activities, classroom work, projects, you name it - and groups these skills by category of skills that relate to the kind of job you're seeking. This format works best when a traditional resume just doesn't work to make you look like a good candidate even though you have relevant skills. A Career Services advisor can look at your first resume draft and help you decide if a skills format might be the best approach to use.
Look at the samples, and the features of each. Choose the combination of features that matches your background. DON'T choose a resume style simply because the fictional student in a sample has your major. Students in any major can use any resume style. You may choose any style regardless of the type of employment you are seeking, whether internship, part-time, or permanent employment. DO choose a format which best shows how your individual credentials support your objective. If you are unsure, start with a chronological style (the most traditional), have your resume critiqued, and revise your resume as needed.