You dont need to have the EXACT same brand of card, it should work just as long as the core's clock speeds are the same (which they most-likely will be).
All you need to do is find out whether or not it comes with a crossfire connector (I dont think that any of them exist without one to be quite honest)
You are getting the EXACT same video card if the one you mentioned on the bottom of your post is the one that comes with your PC. The only thing is, they might give you one that has a different cooler (They are the exact same card though just with a different look... this shouldn't effect the preformance)
OR you might get the exact same one as the other you already bought.
I have my second xfx 5770 being delivered in a day or so from newegg. It's exactly the same one as I previously ordered. I was going to get the one from best buy but didn't want to drop the extra$50 for tax and the big box price. You'll be fine with that extra card you ordered, but it won't come witha crossfire bridge, I'm almost 100% on that. Go to xfx's website, make a support ticket requesting a crossfire bridge and they'll mail one out to you. I got mine in 2 business days.