Near as I can figure, just the model number and the likelihood that one is sold at a specialty shop whereas the other is sold at regular stores. However, I would call and complain and let them know about the error. If the 882 has LCR preouts and DPL II it should be identical to the 1802.
They are the same unit, however it is still wrong that they sent you something different from what you ordered. I would like to know who you orded it from so I can avoid that internet retailer. You should definitely call the vendor and give them grief and see where that goes, hopefully you haven't opened the denon box depending on how your call goes.
I would return the '882 and insist on receiving an '1802. Even if the dealer tells you they are the same receiver, insist on an exchange anyway. Just because the receivers are identical on the outside and have the same feature set doesn't mean they are the same on the inside. Maybe the '882 uses cheaper parts inside. It's possible. You should call Denon to see what they have to say about this. If they are identical receivers in every respect, then why use different model numbers?