You are correct, the required education for both is identical in length. In both cases you complete bachelor’s degree and medical degree, followed by internship/residency/license to practice as a general practitioner. Then you return to med school for coursework in the area of specialization, followed by internship as anesthesiologist or radiologist, followed by board exams. Then you are ready to practice one of them.
Your undergraduate major–what college you attend will not matter. In fact, I’d recommend that you start at one of our exceptional public community colleges in Ohio and then transfer to one of the state universities. It will be important for you to graduate with little student loan debt; medical school graduates nowadays are starting their careers with so much debt that the dean of one Ohio medical college recently went public with his concerns that some doctors will never get out from under those debts.
Your major could be anything, really. Pre-med is the most logical one, but medical colleges claim that they like well-rounded students. So if you do pre-med, make certain you use your electives and extracurriculars to show breadth–take a lot of arts and social sciences, participate in non-medical-related activities. OR, major in anything you like, but use your electives to cover all the science and math courses that the pre-med majors are required to take.
Of course, be serious and generate a high GPA. In your junior year you’ll take the MCAT admissions test; make sure you hammer it!
One other thing you can do to promote your chances of admission to med school: get personally acquainted with some doctors. One way to do that it to work (volunteer or for pay) in a medical setting–get a part-time job at a hospital or volunteer at a health clinic. Let the docs know that you want to become one of them, and when it’s time, they can advise you about which medical schools are best (if I were choosing, I’d try Ohio University and do their DO program), they might tell you what to expect in your med school admissions interview, or they might write letters of recommendation for you.