I have, in my "working" library, the Modern Catholic Dictionary, written, or at least compiled, by Father John A. Hardon, S.J.. This was published in 1980. It claims to be the first new Catholic dictionary published since the second Vatican Council.
Its amazing what you can find in the "Dead Book Sale" of a small community college.
I found four entries to be quite interesting, those on faith and belief and those on intellect and reason.
The relationship between these pairs is, to me, fascinating. Briefly, faith and belief have to do with the acceptance of another, trusting that they know what they are talking about and are being honest in what they are saying. The difference between them is two-fold: 1) Faith has a stronger level of trust than belief, 2) Faith is an act of of the mind whereas belief is an act of the will.
That second part is really interesting. Belief is without recourse to reason, it is only an act of will (not in the occult sense). Faith, though, is much more, it is not just an act of will, though it is that, it also requires employment of reason. This reminds me of Medieval and Renaissance traditions, both Jewish and Christian (and I'd imagine Muslim as well) that support of reason is necessary for any real understanding of God. The requirement of reason for faith also pulls it away from popular uses of the term that really suggest "blind faith", which is now nearly a contradiction of terms.
Intellect and reason stand in a similar relationship. Reason is a process through which we analyse and employ evidence. Intellect, though, is the faculty through which we recognize truth, regardless of a process of reason. It is still a way of thinking, but one that transcends the necessity of, or recourse to, the senses or imagination. A kind of gnosis.
The mystical theology of the desert father Evagrius Ponticus describes a spiritual process that moves from faith to gnosis, with gnosis being the culmination of faith.
I don't really have a point to any of this. I just thought it was interesting.