Interestingly, Lewis and Short give both heart and mind as possible translations for either word.
We tend to associate mens primarily with mind (English derives mental etc from this root). Cor certainly means heart, anatomically speaking.
It all started because I translated (provocatively)
Oremus: Gratiam tuam, quaesumus, Domine, mentibus nostris infunde;
The traditional (and better, I would argue) translation is Pour forth we beseech thee O Lord, thy grace into our hearts.
But the discussion set me off thinking about the link between mens and gratia, as found for example in O Sacrum Convivium.
And I have just remembered another, the Veni Creator Spiritus, where we find:
I am not sure what conclusions, if any, one can draw from these examples. I think I will continue to collect them as I come across them, and hope that while I procrastinate, someone better informed than I am will offer some wisdom!