Bought external drive and installed into MacBook Pro (unibody) mid-2009!
Yup, can take the drive out and it's a SATA drive.
Over the weekend, I visited the local electronics market (I live in Taipei) and did a bit of research. The Backup Plus Slim portable external drives from Seagate (at least the STDR200010x and STDR200030x models, where "x" denotes the color of the case) still house the Samsung M9T 2TB SATA interface drive, part number ST2000LM003.
Here in Taiwan, the bare drive isn't available -- I only found it online from a single vendor and selling at roughly $230USD -- while the external drive version is sold nearly everywhere for $115USD.
For me, the real anxiety was in whether the drive inside had the SATA interface, because I'd read (and my IT guy warned) that Hitachi and a few other makers were starting to put drives that had a different interface into their external drive enclosures (perhaps to cut costs, perhaps to avoid people like us taking them out and using them as internal drives, don't know).
I have some photos of the process.
The slim case is pretty tough to get off, but you take a flat screwdriver and gently pry the aluminum cover off. Start around the edges AWAY from the USB3 port (that side is held in by "clips" and also sticky tape, so it's the toughest edge). Hopefully, my images show you the clip locations. That SATA-USB3 interface circuitry also took a little finessing to get off, and I'm not sure if I had to peel off the foil/grounding wrapper, but I did anyway.
Of course, the warranty is shot now, I think, though I didn't remove that "WARRANTY VOID IF REMOVED" sticker. Oh well.