International Relations is one of the four major subfields of Political Science (the others are Political Theory, American Politics, and Comparative Politics). Many school also offer interdisciplinary majors in International Relations or International Studies. In addition to core courses, IR/IS majors usually require a student to select a thematic focus (e.g., national security, international economics, development, etc.) and a regional focus (e.g., Africa, East Asia, etc.). Usually, study of a relevant language (and, study abroad) is part of the requirements for each regional focus. Some universities have a professional school of international relations, which might place more emphasis on policy issues or which might include some project courses. Some of the professional schools offer undergraduate programs, but most commonly these are graduate programs. A few schools have a separate IR department.
Across different colleges and universities, undergraduate programs that focus on some aspect of IR/IS come with a wide range of titles (e.g., global studies, international studies, development studies, international relations, pace and conflict studies, etc.) and structures (including majors, minors, certificates, and subtracks with majors). These are in addition to the various interdisciplinary language and area studies programs that focus on a specific country or region (e.g., Russian Studies).
You would not necessarily benefit more from a political science major than an IS major. It really depends on your interests and career plans. If you want to study aspects of political science other than international relations and comparative politics, then you could do a double major in political science and IS. You also could just use electives to choose courses of particular interest without doing a double major.
Also, see my posts in this thread:
http://talk.collegeconfidential.com/other-college-majors/902677-political-science-vs-international-relations.html