Is an MD the equivalent of what we would call a family doctor? The local doctor you go and see for all sorts of ailments? If so, is that 800 dollars for a sort of intake talk plus first consult and 400 dollars for each following consult? Does that include other thing like medications?
In the US, MD stands for Medical Doctor. Most of them pick a specialty. Internal Medicine is for adult general practice, and Family Medicine is for both children and adults. Those would be what the UK calls "GP" or general practitioner.
Any other doctor is also an MD as long as they went through medical school and completed their apprenticeships.
There are now "functional MD" 's who are usually general practitioners but might be from any specialty (gastroenterology, etc..). These don't accept insurance because Insurers require them not only to negotiate on price, but also to meddle in daily decisions. Insurers publish CPGs, clinical practice guidelines (other regulatory agencies do too), and these often gag doctors and bind them to specific actions that the doctor may not agree with.
I think functional medicine started up around the same time as we completed the Human Genome Project. There was so much new medical data, and so little of it was filtered through the education process given to doctors. Many people started saying that clinical practice was falling behind science. And that where clinical practice was being updated, it was done to benefit pharmaceuticals without much regard to helping patients.
Generally when I have seen a functional medicine doctor, which isn't often, the first visit is long while we cover most of my medical history and then tests are done. The tests and supplements/drugs recommended are a separate cost. So when I said 1200 for the total to get any value, I was referring to 800 for the initial visit and probably around 400 for tests and supplements or drugs.