Does the iPhone 4S and 4 have the same back?

My iphone 4 back busted and my friend has a iPhone 4S back. Both are GSM will the 4s back fit my 4?

I thinks so because they can use the same cases and everything, but you can buy another one online

I'd think so, but I think you are safer trying to get a 4 back plate specifically because of the slight external differences between the 2.