I thought I could chime in with a couple comments.
First off, there is a neuropsychiatry dual residency possibility in which one becomes boarded in both psychiatry and neurology. We've had semi-extensive threads on this in the past, but I can sum it up by saying that this is a very interesting and lucrative field. Theoretically, a neuropsychiatrist specializes in conditions and syndromes that are likely neurological in nature, and have psychiatric sequelae. Not to create a mind-body dualism, I'll provide an example:
Post-TBI patient who develops personality change, seizures, and is suffering functional loss.
The neuropsychiatrist would be able to treat this person comprehensively (i.e. the seizures, brain recovery, and psychiatric symptoms).
In practice, neuropsychiatrists treat seizure disorders, may conduct EEGs or EMGs, see and manage Parkinson's, Huntington's, and all sorts of Parkinson'g Plus syndromes, and lots of other stuff.
When it comes to psych-med vs. psychosomatic, one must realize that simply completing a psychosomatic medicine fellowship will not really put you on track to practice internal medicine. To borrow from the American Academy of Psychosomatic Medicine, a definition of a psychosomatic medicine specialist could be: clinicians dedicated to the scientific understanding of the interaction of mind, brain, body and social context in promoting health and contributing to the pathogenesis, course and treatment of disease.
One could see how this is different from psych/IM residency, which will basically allow one to be boarded in either, and in most cases, have you practicing psychiatry (likely in a hospital setting), and manage medical problems concomitantly. There are also Med-Psych units which employ these types of physicians. These units are basically for medically sick psychiatric patients, and often incorporate end stage dementias and the like.
Hope this helps.