Those are some very good questions and I'll do my best to answer them as best I can. Sorry it took me so long to reply but the medical school decided to give us a full day of hints/tips on being a successful junior doctor before we start our 'shadowing' placement tomorrow.
Those definitions are basically true but as I'm sure you guessed they are very oversimplified. There is overlap in these professions - most Psychiatrists do research in the field (although this is usually more clinically orientated than the research psychologists do) and as I mentioned before some Psychiatrists become 'Medical Psychotherapists'. Although it is quite rare in the UK for Psychiatrists to do psychotherapy full-time, the GMC is starting to incorporate at least one placement of psychotherapy into the specialist training for Psychiatrists. And many Psychiatrists will do CBT as part of their work. Unfortunately I don't have much experience with the American Psychiatric profession but as far as I'm aware there are quite a few Psychiatrists who go into private practice as a Psychotherapist.
I don't really know the numbers of psychiatrists compared to psychotherapists on the NHS but each GP practice usually has at least one counsellor on the staff. I think the most important thing to know about the numbers of professionals is that they are all hugely understaffed. The GP practice I was placed at before my exams had up to 10 months waiting lists to see their counsellor (this is normal throughout the NHS) and even with taking on large numbers of doctors from outside the UK, they still only manage to fill about 80-90% of Psychiatry training places. There are also major problems funding psychiatry in the UK due to the nature of socialised medicine - at the community mental heath practice I worked in last year the two Consultant Psychiatrists were told to either take a 50% pay cut or one person had to take early retirement.
There are lots of types of psychotherapy such as psychodynamic (similar to psychoanalysis), CBT, CAT, family, group and many more. If you are interested I can find you a book explaining about psychotherapy?
My current plan is to do my two 'foundation years' of general medicine, which should start in August (assuming I pass my exams) and then do something in the private sector - I haven't really decided yet but working for a start-up in biotech sounds like an interesting career - although that would require doing a masters degree. I hope that answers the last 2 questions.
I'd be interested to hear your opinions about psychiatry / psychology and your experiences so far as an engineer?
Thanks,
James.