In the US, MD’s and DO’s are legally equivalent. My understanding is that osteopaths in the UK are more along the lines of chiropractors. I think that in the us they prefer to be referred to as “osteopathic physicians” to emphasize their practice of conventional (Western) medicine.
The main difference in their training is during the preclinical years, when the DO students recieve training in Osteopathic Manipulative Medicine, which I belive is similar in many aspects to chiropractic. After medical school, apparently very few US DOs incorporate OMM in their practice.
Medical school and osteopathic school are both four years. DO students are eligible to take the USMLE, the allopathic licensing exam, as well as having their own test, the COMLEX. Some take both, some only take the COMLEX. I believe all 50 states accept either tests for the purposes of granting medical licenses to DOs.
Residency is similar. Some DOs go through the same residencies as MDs, and some go through the separate DO residency system.
These days, the main difference between MD and DO students is their attractiveness as applicants. DO schools tend to be less competitive for admission. The average DO school tends to have an average MCAT score of their class that is about 5 points lower than the average MD school, and the average GPA is also lower. Many less competitive applicants apply to both MD and DO schools. Students who apply to DO schools because they believe in osteopathic theory seem to be in the minority.
I am an MD student, and I have no problem with DO students referring to themselves as medical students. We’re both going to be doctors. There are a number of DOs who are faculty at the school I attend. Several have lectured to my class, and I can tell no difference in their knowledge vs our MD lecturers.
I have also worked with some of the DOs on faculty in different volunteer positions, and all that I have met are excellent physicians. For a physician for myself, I would consider the physician themself and not really consider their degree. I do not think which medical school they were able to get into based on a single test grade predicts what kind of a physician they will be.
Quackwatch gives an overview of the history and theory of osteopathy in the US, as well as examining some of its more dubious aspects, the practice of which seems to be decreasing.