I'm looking at a job application that asks for the following:
I find this confusing because I don't understand what a "Statement of Interests" is supposed to be, relative to the others. Does anyone know what's expected in a document of this kind? I'm a bit shy to ask the institution in question just yet, for fear that it's something well-known.
That is a rather confusing request, actually. However, what I think the job offer is looking for in a "statement of interests" is a description of the research areas you are interested in, while the "statement of research" would be a listing of projects you'd plan to start if you were hired.
However, in many job postings, those two items would potentially be conflated into a single statement. So I'd recommend that you contact the department. I'd recommend doing this by phone, if possible—that way, you don't have to give as much identifying information.
Since I assume it is an academic job you apply for the letters will cover aspects of that type of work. The job profile could possibly also reveal how to interpret the requested information. My general advice concerning the confusion is to contact the employer to get additional information (they may also keep such information on a web-page). It seems the instructions are sub-par in this case, which is annoying.
View the CV as the back-bone and the statements as an opportunity to provide some meat.
aeismail has already covered two of the letters/statements well. How the research statement should be interpreted is less clear, but posdef's comment is good because it may concern what you have already done. If it is then it is common to go through previosu research and highlight what you consider are your major contributions out of your production and how you consider your work original and contributing to development in the field(s) of concern. I would strongly advice asking about the focus for this letter.
The statement of teaching is usually detailing your views on teaching. The purpose is to get a sense of your ideas and understanding of pedagogical aspects of the work. This may nclude techniques/methods you have already used or ideas on such that you wish to develop. It could also include ideas on courses you would like to develop (if you have a sense of your possible coming mandate at the place at which yo apply. If your position is not concerning teaching, such a statement may not be necessary (I assume you received a form letter?). But, if you are pplying for a position which includes teaching then such a statement may be quite important and provide the job committee with a firm picture of your teaching philosophy.
