If your replacement iphone was sent to you in plastic wrap and in a smaller box it was more than likely a refurbished phone. When I received my refurbished phone it came exactly as you described and was a refurb. If it is a brand new phone they should send you an email with you new warranty. If you don't receive this, the serial number is updated in their computers and provides you the refurbished warranty.
I am just speaking from experienced when I had problems with my 2g iphone, they sent a refurbished...I different problems with this one. I spoke with att and they apologized for what I had gone through and told me they would send me a brand new 3G iphone, I happily agreed. When the package arrived I received a brand new 3GS with new ear buds and charging cords. The next day they sent me an email with proof of warrant on my new phone. So if you didn't receive the same thing as I did chances are its a refurb (not that anything is wrong with refurbished items).