To me (for me), to “believe” is a cognitive process that brings one to a conclusion based on concrete and observable evidence. The question of what constitutes “evidence” may clearly vary from person to person. For example, a Christian (or other “believer”) may look around at nature, ponder the celestial heavens, etc., and accept that as evidence that a diety (God for me) is a reality and that is evidence supporting that idea. An atheist may observe the very same things and conclude cognitively that is not evidence of anything except the universe exists (assuming, of course, he/she doesn’t believe it is simply an illusion). So, in the end, belief is to a greater or lesser degree a very subjective process. One “believes” what one believes. Consensus on the validity of a belief is not a necessary element of whether or not ones belief can be regarded as a belief.
Faith, on the other hand requires no such evidence and at least on some level may actually amount to a simple “choice.” This could be very true for someone in the early stages of conversion. My thought is based on the fundamental concept that God is constantly drawing everyone to Himself. I believe a “choice” to exercise faith may simply be an affirmative response by an individual to that without an awareness that God is the source of the choice. In this case, of course, we could say that even this sort of rudimentary “faith” is a gift from God. At some point, hopefully, the individual grows in the experience of a faith community and begins to receive the gifts and affirmations that lead to and foster authentic beliefs. Referring, for example, back to my previous comments on “evidence,” the individual comes to a point where he/she accepts the experiences of the universe as evidence of God’s creation and God the Creator.
This is how it comes together for me. For others? Who knows? Pray for an increase in “faith,” but in the meantime make a “choice” to have faith that God is real. A nurtured faith can lead to real “belief.”