I think the distinction between appreciation and enjoyment is a really interesting one. To me, they're extremely similar. If I can appreciate how something was done, I'm going to enjoy it so much more. And the context plays a huge part in that, in informing my appreciation. Take film, for example. There are lots of films I didn't particularly enjoy the first time around - take Werner Herzog's Aguirre, for example. Really didn't enjoy that, but after studying it and rewatching it for the contextual and filmic elements I really did enjoy it, because I could appreciate it and understand it more. I can see how this isn't going to be true for everyone, though.
I think it really depends. The two are indeed separate for me. Sometimes they line up, and sometimes they don't. In some cases, knowing "the secret" behind it kind of ruins it. Movies and Video games are especially vulnerable to this (considering I know a bit about how they are made). Music is a bit different, as I don't know quite all the details about how it's made. So it's mostly a naive view, followed by learning about the music later on. A good example (for me) is Eminem. I don't really like his stuff. At all. There's maybe a song or two that I enjoy. But after reading up on the guy and listening to some interviews, I can kind of "see" him behind his work. So I appreciate it a bit more. Doesn't mean I like the music though. It still "sounds" the same, but I have a greater appreciation for it. In other cases, I find that learning about the history/context adds to my enjoyment. That's rare though :P.
For me, knowing "the secret", as you put it, almost always improves the thing for me. I love that, personally, because it means the more I get to know it or the person who created it the more I can enjoy it. Hip hop is a good example for me, too, actually. I never really enjoyed it until I started getting into different parts of the genre - Home Brew specifically. At first, I just enjoyed their lyrics and political content (*very* local) but then, the more I listened not just to them but to similar stuff the more I could appreciate the production and how it all works. It changes the way it "sounds" to me, too, because now I can tell when a track has been produced really well - or, even better, really interestingly - and I can enjoy it a lot more. Like I said, it's really interesting how this is different for you. Context and perspective is fascinating.