Actually, you are correct, "διάνοια/dianoia" is more accurately translated as "mind". But to clarify this it will take some explaining. Hopefully, I will not mess this up!
Bear in mind, that the theology behind this is purely eastern, based on the terminology used by the Early Church Fathers and especially by the Desert Fathers who practiced nepsis ("watchfullness").
"Nous", as used in St. Paul is what the later fathers distinguished as "dianoia". Dianoia, literally means "through the mind" or "with the mind", and it is referring to our thoughts, our reasoning, our mind, our intellect. In St. Paul the word nous is used instead. Nous is based on the verb "νοώ/noo", which in ancient times meant using your intellect. St. Paul is using that term and contrasts it with "πνεύμα", translated as spirit. Later, and through the discourse between Greek philosophers and the christian fathers of the east, the term "nous" shifted towards the philosophical greek meaning, esp. of Plato and partially of Aristotle. Plato contended that nous was an immortal part/function of the soul, which understands truth, reaches conclusions without need for explanations. This is quite similar to the concept of the enlightenment of the Holy Spirit after catharisis (purging of the passions), practiced by the fathers, so they used that term instead to clarify what really happens to the greek philosophers who sought them out. Consequently, in their writings this change is gradual, and sometimes the terms "dianoia" (intellect), "nous" (intellect OR core of the soul) and "pnevma" (spirit or as St. Paul used it, core of the soul) are interchangable and it can be confusing, especially at the first 300 years of Christian writings, later the terms are solidified: dianoia=intellect and nous=core of the soul.
So, to summarise:
We have two different things. 1. The intellect and 2. the core of the soul, which according to the Fathers, is the "deep heart", the nous, which is the organ that communicates with God, the place the Holy Spirit dwells, which after the Fall is clouded and we need to follow the narrow path of Christ to re-open.
What is interesting is that our intellect is not a brain function but a function of the soul, according to the Fathers and surprisingly to the ancient Greeks as well (mostly). Through the nous is how we think, how we examine, how we intellectually understand. The problem becomes when the dianoia and the heart are not in-tune so to speak.
Example. We say we believe in God, but the Fathers would say that this is an intellectual assertion. We intellectually accept that Christ is the Son of God, but in our hearts, nous, we *cannot be sure*. Which is why the Fathers distinguished between two kinds of faith. The faith of the dianoia and the "endiathetos" (the inner stance roughly) faith. An example of scripture for this would be the father of the boy to Christ: "Lord, I believe! Help my disbelief!", which on its face is an oxymoron, an antithesis. Yet, he says, I believe you are the Son of David but I need to BELIEVE it in me!" and this is a fine example of how it is God's gift, this true faith...
Anyway, I have drifted a bit and I am not sure if I haven't confused matters more. I would suggest reading someone more eloquent and versed in these matters (which I know more intellectually than experentially infortuantely). A modern Orthodox scholar who is very precise and clear, is bishop Hierotheos Vlachos, who was a student of the intellectual giant, Fr. Romanides.
This essay deals a lot with the subject (including the Logos)
An even better suggestion perhaps, although not as academically prestigious, is the book
The Way of the Pilgrim. It is a book that deals solely with the prayer of the heart, the practice of the Desert Fathers, and how it leads to illumination of the nous by the Holy Spirit. Written by an anonymous man, it is simply his narration of his journeys and quest for an answer to the scriptural "pray without ceasing" (I Thess. 5:17).
Hope that helps! It is a rather complex matter filled with definitions and it's a bit difficult to convey it in a small post.