Is the capacity of a Refurbished iPhone 4 different?

I just bought a refurbished iPhone 4 IOS 5.1.1 and purchased extra storage for iCloud. Prior to the 4 I had an iPhone 3 with 13.6GB, this 4 shows a capacity of 6.4GB and the box it came in (marked refurbished on it) says 8GB.

So exactly how much capacity does a refurbished iPhone 4 should have, because if this is all I'm getting, I'm returning the 4 and going back to my 3.

Any help would be appreciated. Thank you.

Kim