"Board exams" = United States Medical Licensing Exam (USMLE) Step 1/2/3 -- emphasis on the "United States" part. Once you take and pass all three parts, you're set.
Specialty boards (for the specialty in which you complete a residency) are also nation-wide. You take these after completing your residency and take re-certification exams every 10 years.
Moving states from a "legally allowed to practice" angle isn't difficult, it's just expensive and time consuming. For example, I'm moving to California after my internship and the process of getting a license will probably take ~6 months and cost about $800.
Requirements vary by state, but generally they require a certified copy of your med school diploma, USMLE scores, and certificate from your internship and/or residency. Foreign grads require extra documentation. Your specialty does not impact your ability to obtain a license in a different state.
Now establishing a practice is a different can of worms. If you are moving to an area with a big need (i.e. primary care in a rural area), your new employer/group/hospital may pay for your fees and help your jump through the hoops of getting licensed, but the steps to get that done are essentially the same.