You're confusing the Kindle serial numbers and ASIN numbers which isn't too difficult considering both start with B and look fairly similar.
ASIN means Amazon Standard Identification Number which are basically stock codes. Each distinct product that is sold on an Amazon site would have its own ASIN to identify it. Most items have an ASIN that starts with B but real physical books use the ISBN number instead.
Kindle serial numbers all start with B and the 4th character shows what model Kindle it is.
If you buy a Kindle via mailorder on the regular Amazon site then they're shipped like how you received yours. They don't have an outer box that contains the Kindle box and the shipping label is stuck to the box directly. It doesn't have Amazon Kindle in big letters over it. It does mention Kindle on the small copyright line on the bottom and the person reading a book logo is part of the barcode. This new packaging for the Kindle 3 is part of some green packaging initiative by Amazon. I can't remember what they actually called it though...