You bring up a good question, and my initial reaction was that faith and trust are one in the same. It’s almost a grammatical distinction. I can’t faith someone, I can have faith in them. If I have faith in them, I trust them. I think we tend to use trust when we’re relying on someone for something, but we can have faith in someone when we’re not relying on them for something.
I’m interested in your distinction, saying that putting faith in something requires “something stronger”. I wonder if you can explain that a bit more.