It's unusual that someone does both fellowships, but there is so much overlap between the two areas that there are many docs who hang out this kind of shingle--it is more usually an internist, anesthesia or rehab doc who treats a lot of chronic pain and who has become certified as an addictionist through American Society of Addiction Medicine (ASAM), as opposed to an Addiction Psychiatrist who has done Pain. (I explained this in another recent post.)
ASAM does a biannual "Pain and Addiction: Common Threads" symposium that can be really useful. Check out their website at www.asam.org.