Short answer I believe is: Yes you will take 4 different flight physicals, generally speaking. There used to be(may still be) a method in place for Service Academy accessions as well as ROTC scholarship candidates called DODMERB(Department of Defense Medical Examination Review Board). Essentially the summer prior to joining or during the application process you would take a standard physical, normally with a civilian Dr or Medical Treatment Facility if available. The Medical records are then reveiewed by DODMERB and given thumbs up or down or additional appointments were needed if something came up that raised an eyebrow. This was to ensure candidates met basical phsyical qualifications for service.
The services all have different standards for their aviation(aircrew) programs and thus have medical staffs trained in those standards requiring different physicals. I do know that exchange pilots coming to the Navy for instance, don't take a flight physical when they check in, but rather have their medical record reviewed by a Flight Surgeon and medical clearance is then issued, but I think it's safe to say that if you're applying for ANG, Navy/Marine OCS or the Army you may indeed need to take different physicals for the different services before you are accepted into any one of those programs.
Someone with a bit more recent experience here may be able to shed some more light, but if I were a betting man, I'd plan on having to do a physical for each of the Services you apply to.
Good luck.