MBBS is Bachelor of Medicine and Bachelor of Surgery. This is the qualification needed to practice as a doctor in the UK. It is exactly the same as an MBChB and others, just different variations of the abbreviated latin.
In the UK, MD is essentially a postgraduate research degree similar to a PhD. I might not be exactly right in saying this. I'm sure someone can correct me if I'm wrong. In the USA, however, doctors are awarded an MD instead of the above MBBS/MB ChB etc.
Bachelor of Medical Science is just an undergraduate degree. It's just a variant of a BSc in Biomedical Science as far as I'm aware. They are not doctors.