Different Statement of Purpose to the same advisor in two programs? First I have to make it clear that I understand the SOP is not just written for my potential advisor to view; it will certainly be presented to the admission committee first. However, my potential advisor will be the only person who reads both of my SOPs. Below is the complete question with background information:

I am currently applying for psychometrics in both Department of Educational Psychology and Psychology (Quantitative psychology) in the same university. My potential advisor is a faculty member in both departments, doing research on XXX. When I wrote my SOP for psychometrics in Educational Psychology, I only talked about my research interests in XXX. 

Now I am adapting my SOP to application for Quantitative Psychology which allows students to do research in collaboration with other fields in psychology in addition to their own research interests. I am interested in doing research in the Social Psychology and am considering if I should include this in my SOP, given I only mentioned that I am interested in XXX in my SOP to Educational Psychology? In addition, XXX is really different from social psychology in general..in other words, my two research interests are not relevant.

As my potential advisor will be reading both SOPs, I am afraid that having talked about additional research interests in my application for Quantitative psychology would make me appear not firm about my research interests in XXX (am I overthinking about this?) Or is it even necessary for me to mention my research interests in social psych in my SOP, as I will be given opportunities to work on research in other fields of psychology, including social psych, anyways?

Additional information: my potential advisor knows that I am interested in social psychology as I mentioned this to him. Nonetheless, we never had a talk about my research interests in social psych.

In short, 1) do I need to talk about my research interests in social psych in the SOP to Quantitative psychology? 2) if I do, what's the best approach to avoid my advisor feeling confused about my research interests? (for example, just vaguely mention that I would be excited about doing research in social psych etc. ?)
Yes, it's totally fine. Its absolutely normal to apply for multiple positions and obviously promise them that you will do things that are unique to them if you are accepted. This shows that you have twice the interests and also ideas on how to fit in aside from determination. 

1) Do I need to talk about my research interests in social psych in the SOP to Quantitative psychology?  Yes, as much as you want to mention possible cross-disciplinary researches but not too much. This should be 10-20% of your SOP. The rest should be really aligned with requirements of each program and the possible dissertation committee members from each group. Think of your dissertation topic and board members in each scenario and write for them as audience and signer of your dissertation. 

2) if I do, what's the best approach to avoid my adviser feeling confused about my research interests? SOP is not a marriage proposal. It shows that you have interests in both fields and work and degrees. And you really want to be in that school. He will not feel betrayed or anything. If anything he should see how much you are interested in the whole field. Don't deny that you have skills in both fields though. There should be some 10-20% overlap. but you are proposing a whole new direction and possibility of your dissertation work. 

Big assumption: universities don't really want you to be firm on your research interest when you are not even accepted yet. And even after that there might be no funding to some topics, so you might have to do other stuff. Research is just another industry that is limited to its resources and can not be idealistic about constraints. Meanwhile, they love to see applicants with muti-dimensional skills sets and openness to cross-disciplinary research. But beware of not looking focused on each of these SOPs.