Quick answer for your question.
HTPC is simply that, a computer hooked up to your home theater. It has the same function as any computer would for your purposes, from web browsing to high res gaming to big screen graphic design.
A media server only distributes files over a network. It will require something to play them at the streaming end, like an HTPC or a media streaming device. A server only holds your library, collection, content, whatever you want to call it.
Hope that illustrates the difference well enough.