Faith is a subset of belief, as you say. Faith is always belief, but belief is not always faith. You seem to flip flop between the two when you talk about science. I'll try to demonstrate from my point of view what the difference is (since I love science and still think there is a god).
I don't have faith in atoms. The only reason I believe in atoms is because of the evidence. They don't effect my daily life in any way. The fact that my desk here is made of itty bitty little bits of bits that are itty bitty does nothing to change my desk. If I had never been given evidence of atoms I would not have cooked the idea up on my own out of desire, or hope, or want. I don't care about atoms at all. If some smart chap comes out with a theory tomorrow that gives a great explanation as to why atoms don't exist, I'm all for giving the idea a shot. Because if atoms aren't real, so what? By the way, "Scientists might be lying." is not a good theory by a smart chap.
Faith isn't like this at all. I do have faith that god exists. This has everything to do with me wanting it to be so, and absolutely nothing at all to do with evidence. Nobody found god and said, "Hey look at this!" and I said, "Oh, nifty. What's it do?" "Nothing." "Huh. Game on Saturday looks good." No, I decided there is a god and it has a profound impact on the direction of my life, my thoughts, etc. Because that's the way I want it to be. No other reason matters. That's faith.
Just my opinion of course.