I don't disagree with your characterization of a 1st degree versus 2nd degree faith, although I do believe that even though they contemplate different things, they manifest in the same way: believers don't need evidence to prove whatever the thing is to them, because they already believe, and that's enough.
And besides, it could be fairly hypothesized that most, if not all, faith is is what you refer to as 2nd degree, since it is one's social circle—starting with the family and extending to neighbors, friends, classmates, co-workers, fellow congregants, whatever—that ratifies your faith through social approval along the way and validates it as an idea and, by extension, you as a person. I think this is particularly true when it comes to faith in a god, because that gets taught to you by your family from a very early age during the initial socialization process. Very few people if any come to believe in a god without any information from outside, and I highly doubt that without that outside information, that practically any child would start questioning their place in the universe and seek to place their belief in a supernatural being.