I'm not proficient in Latin by any means, neither am I a linguist, but I'd like to give my two cents on the matter.
When I was traveling around Italy, I was a bit confused when I first saw Church inscriptions that used the word "divus" when referring to a saint (here, and here). The only Latin word for saint that I'd heard up until that point was "sanctus", since it is the word that's used in the Litaniae Sanctorum and in most of the Latin prayers that I was familiar with. Also, in the Roman Missal, I don't recall ever coming across the word "divus" when referring to a Catholic Saint, but the word sanctus is mentioned many times during the Canon Missae, for instance. This means that the word Sanctus was probably the preferred term that was used in the official prayers of the Church.
That being said, I believe that divus was a less precise term that was used in some ecclesiastical circumstances (i.e., Church inscriptions) as an equivalent of Sanctus, probably due to the fact that during the Roman Empire the word divus was not only used for pagan deities, but it was also used as a sign of respect for the emperors. Therefore, it might've been the case that throughout the Middle Ages the term divus was used as a synonym of sanctus and was devoid of its original pagan meaning. Finally, the fact that there wasn't a big controversy over the theological significance of the word "divus" means that the word probably lost its original meaning and most people just considered it to be a word that was entirely separate to the Latin word for God.
Here is an example of the words divus and sanctus being used interchangeably when referring to a Catholic Saint. Also, this might be a coincidence, but most of the times when I saw the term divus being used, it was connected to the name Francis (i.e., Divus Franciscus, Divus Franciscus Salesius, Divo Francisco a Paula, etc.).