Faith and belief are distinct.

One places his ‘faith’ in a person, a someone, and then ‘believes’ in what he says.

In Christianity, one places faith in the incarnate second Person of God, and then believes all that He says through Scripture and Tradition formulated in the doctrines of His mystical body the Church.

‘Believing in God’ means very little. The devil believes God exists; but he refused to have faith in Him.

While faith includes the mind, it’s ultimately an act of the will.