No, it’s not the same thing. You can simply put “© 2013 – All Rights Reserved”, which is pretty self explanatory. You reserve all the rights to the content.
The design of the site might be an issue and is more complicated than slapping a copyright symbol on it. Such as, you can’t copyright CSS or HTML and since CSS is what is behind most of the design, you’re pretty much screwed. However, there have been legal cases (one which you can find on Wikipedia under “Trade Dress”) regarding stealing a website’s design.
If it’s artwork, I’d suggest to your client that he/she registers it.