Well, "website hacking" is still hacking into a system; most exploits on websites are done to the point of gaining full access to a webserver (and in a lot of cases, people would hack the server itself to deface a site).

I guess my main question is to you; what exactly do you want to do?

My first suggestion to you would be to go read up on some security white-papers, go look at what is patched in a system (such as many of Microshaft's tuesday security updates), and go delve into what they patched and try to find how they patched it (and what was done that they had to patch). A lot of the time you won't be able to find much information on it, but a lot of the time you can find exactly what went on through a whitepaper.
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