No, they're different. I was just in BRU last night buying a pg support band because I have been in so much pain. The support band lifts the belly a bit and gives it structural support where the muscles are having a hard time doing. Just an hour last night in it took care of the muscle pain I was having. The one I got doesn't actually cover my belly at all - it goes both over and under, and wraps around the back to give me structural support.
A pp band is more similar to an elastic back brace. It's kinda like wearing a big ace bandage around your stomach - there to apply direct and steady pressure while your organs and muscles recover from all the stretching and displacement they did. You can use an ace banadage, but it's difficult to get it to an appropriate snugness without being too snug. Which is the nice things about the premade ones, they velcro on, and are adjustable (to a certain range), so that you can loosen/tighten them as things shift through the day, and not feel like you're wearing too-tight pants. Just make sure you get the right size for yourself. I know BRU allows you to try them on (over your clothes), but they don't carry a wide range of sizes. I got the only size Lg support band they had in the store last night, and the girl said she was surprised because they don't normally even carry that size in-store.
As for the hospital list (some of which may also apply to a BC), something to keep in mind, aside from everything else is stuff for your DH/DP. I know the hospital we were in for DS1 barely fed me, they sure didn't feed him. If we had realized we were going to be there for 3 days, we would have planned differently, but we never even thought about it (and he wouldn't leave my side even to go find a vending machine). So pack stuff for him too - toothbrush, razor, clean underwear/socks, snacks, water bottle, and a book or two (. I also would have brought delivery menus from places that deliver to the hospital, since even when they did feed me, it was CRAP (turkey sandwich that was turkey + bread only, salad made of iceberg lettuce, "soup" that just plain canned broth, pasta that was so overcooked it was mush (and microwaved to boot), etc.). Oh, and bring at least 2 sets of pjs/clothes/whatever you plan to wear both before and after. I know at one point I stepped out of the shower (better for me than the tub), and was hit with a bout of vomiting, and vomiting while pregnant typically causes me to wet myself, so the clean PJs I'd just stepped into were covered with pee and vomit. Glad I had another option of something to wear.
Oh, and another thing not to forget is chargers. Cell phone, ipod, CAMERA, anything that needs a charger that you may want to use, bring it. We didn't think to bring the charger for the camera and we ran out of battery long before we ran out of a desire to take photos.
Another thing to remember about the hospital visit - they charge for everything. Pads, tissues, tylenol, diapers, etc. So any of those things that you might question wanting/needing your own, or even if you just object to the markup on it - pack it. I know some insurances don't nickle and dime, but most do, and if it's going to wind up coming out of your pocket in some way or another, that's something to keep in mind.