Is there a difference between writing a recommendation letter for MPhil programs & PhD programs? What I mean is, are there cases in which a professor might decline writing are letter of recommendation for a PhD program, but would accept writing such a letter for a student applying to a MA or MPhil programme? Is the professor seen as vouching for the student more, when he writes a letter for a PhD program than when we're talking about MA or MPhil programs? Or is there virtually no difference?
There may be a distinction between how letters are written for a primarily course-based graduate program and a (presumably more advanced) primarily research-based one.  However, in most cases, it would not be a great difference.  Qualifications such as intelligence, knowledge of the subject area, and reliability/maturity are important for both types of graduate programs.  Most letter writers would probably discuss these issues in similar terms whether the applicant wants to get into a course-based or research-based program.

On the other hand, there are differences between what a letter writer will emphasize when a student is applying to different kinds of programs.  When a student is applying for a research-based program, it will help to have letters from mentors who have worked with the applicant in a research environment, and such letters will carry a great deal of weight.  However, there are almost always going to be several faculty members who can write letters about a student's classroom performance, while far fewer (and often none) who can have worked with a student on research.

There are, moreover, some situations where a faculty member might have no problem recommend a  student for one type of program, but be more hesitant to recommend a student for other programs.  If the student has actually demonstrated that they are good in the classroom but have also demonstrated problems working in a research environment, a recommender might not feel that the student is not ready for a research-based program (like a British Ph.D. program) yet; however, this very seldom happens.