In my trip to Rome, one of the major exhibits at the Colosseum was focused upon Divus Vespasianus. Over at Roger Pearce’s blog he notes a couple of ancient quotes regarding the distinction between deus and divus:
(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.
There is also a good discussion of the deification of Julius Caesar in the comments of this post at Roger’s blog as well.