Both MD and DO are fully licensed physicians who can practice any specialty in all 50 states. The training is nearly identical, with two differences: DO students learn roughly 200 hours of hands-on osteopathic manipulative treatment, and DO programs tend to frame care a little more holistically. MD is the allopathic path and the larger of the two.
You apply to MD schools through AMCAS and to DO schools through AACOMAS, and many strong applicants apply to both to widen their options. DO schools are generally friendlier to nontraditional applicants and to a lower GPA. One caution: only apply DO if you can show genuine interest, ideally by shadowing a DO and speaking to why the philosophy appeals to you, because committees can tell when it is being used as a backup.