Hans Dampf has made a series of very interesting and learned comments on a post of mine about an inscription calling Julius Caesar god. If you haven’t seen these, you probably want to.
In particular he has tracked down and translated two statements by Servius, the 5th century commentator on Vergil, which illuminate the way in which the Latin terms deus (god) and divus (divinity) diverged in meaning as emperors were deified.
I won’t repost all of Hans’ comments, which can be read there. But I will repost what he gives from Servius, discussing “deus/dii” against “divus/divi”, as I think it will be of general interest. The works by Varro etc are lost.
(1) Servius, Ad Ad Aeneidem 12.139 (= Varro, De Lingua Latina fragment 2, edition Goetz-Schoell)
Deus autem vel dea generale nomen est omnibus: nam quod graece δέος, latine timor vocatur, inde deus dictus est, quod omnis religio sit timoris. Varro ad Ciceronem tertio: “ita respondeant cur dicant deos, cum [de] omnibus antiqui dixerint divos”.
Translation: “Deus or dea is the general term for all [gods]. […] Varro to Cicero in the third book [of De lingua Latina]: ‘That is the reply they would give as to why they say dii, when the ancients said divi about them all.’”
(2) Serv. Ad Aen. 5.45 (= Varro fr. 424, Grammaticae Romanae fragmenta, ed. Funaioli)
divum et deorum indifferenter plerumque ponit poeta, quamquam sit discretio, ut deos perpetuos dicamus, divos ex hominibus factos, quasi qui diem obierint; unde divos etiam imperatores vocamus. Sed Varro et Ateius contra sentiunt, dicentes divos perpetuos deos qui propter sui consecrationem timentur, ut sunt dii manes.
Translation: “The poet [Virgil] usually employs ‘of the divi‘ [divum] and ‘of the dii‘ [deorum] indifferently, although there should be a distinction in that we call the immortals dii, whereas divi are created from men, inasmuch as they have ended their days; from which we likewise call [dead] emperors divi. But Varro and Ateius hold the opposite opinion, claiming that divi are eternal, whereas dii are such as are held in honour because they have been deified, such as is the case with the dii manes.