Credo ut intelligam?
A measure of "shell game" is probably unavoidable as the semantic ranges of "believing," "knowing," "understanding" do overlap in general usage and vary from one person, situation and context to another.
Much of our cognitive speech rests on underlying sensorial metaphors: we construe and represent "understanding," "knowing", "believing", etc., as forms of meta-perception: "seeing," "hearing," "feeling," "tasting," "smelling" in some superlative way.
From the Greek tradition metaphors of knowledge and understanding bring the sense of sight to the fore. The intelligible is construed as idea (form, image) and theoria (sight, vision, beholding, contemplation, show). Socratic dialectics leads through logical, rational discourse (logos) from the world of physical perception (belittled as mere appearance or phenomena) to knowledge as meta-vision. The Christian tradition of "faith" is not so different I guess. At first it opposes "sight" (but ultimately also as mere appearance), focuses (especially in Paul) on "hearing" and "responding" (confessing, homologeomai) to a divine rather than rational "word" but ultimately leads to knowledge as "sight" (from "mirror" to "face to face" sight, 1 Corinthians 13). The whole symbolism of revelation (unveiling, apokalupsis, or manifestation, epiphaneia) is overwhelmingly visual. Walking by faith not by sight (2 Corinthians 5:7) is the way (hodos, whence method) to a goal which is still represented in terms of sight.
"Faith" or "belief," or "trust," I think, is the positive response to a call (auditive metaphor) that interrupts, suspends, breaks through, breaks open our sightlike, imaginary worldmap of representations. It is a moment of reception, an opening to the yet unknown (unperceived/unseen etc.) which is essential to the development of cognition. And it depends on literal perceptions (mostly but not exclusively hearing) and their dissonance with the "already-known".
(The miracle story in Mark 7:32ff is highly interesting from this perspective. Note how it plays on the other senses to open the impaired hearing and speaking (which is the usual channel of "faith"): "They brought to him a deaf man who had an impediment in his speech; and they begged him to lay his hand on him. He took him aside in private, away from the crowd, and put his fingers into his ears, and he spat and touched his tongue. Then looking up to heaven, he sighed and said to him, "Ephphatha," that is, "Be opened." And immediately his ears were opened, his tongue was released, and he spoke plainly.")
Without a moment of "belief" nobody would have come to "know" anything.