Old Latin, and Classic Latin are still not the same as 1386 Latin
The old-time language
The concept of Old Latin (Prisca Latinitas) is as old as the concept of Classical Latin, both dating to at least as early as the late Roman Republic. In that period Cicero, along with others, noted that the language he used every day, presumably the upper-class city Latin, included lexical items and phrases that were heirlooms from a previous time, which he called verborum vetustas prisca,[5] translated as "the old age/time of language".
During the classical period, Prisca Latinitas, Prisca Latina and other idioms using the adjective always meant these remnants of a previous language, which, in the Roman philology, was taken to be much older in fact than it really was. Viri prisci, "old-time men", were the population of Latium before the founding of Rome.
The four Latins of Isidore
In the Late Latin period, when Classical Latin was behind them, the Latin- and Greek-speaking grammarians were faced with multiple phases, or styles, within the language. Isidore of Seville reports a classification scheme that had come into existence in or before his time: "the four Latins" ("Moreover, some people have said that there are four Latin languages"; "Latinas autem linguas quattuor esse quidam dixerunt").[6] They were Prisca, spoken before the founding of Rome, when Janus and Saturn ruled Latium, to which he dated the Carmen Saliare; Latina, dated from the time of king Latinus, in which period he placed the laws of the Twelve Tables; Romana, essentially equal to Classical Latin; and Mixta, "mixed" Classical Latin and Vulgar Latin, which is known today as Late Latin. The scheme persisted with little change for some thousand years after Isidore.
So if we really with to be specific, the proper term would be Latina - Latina, dated from the time of king Latinus, in which period he placed the laws of the Twelve Tables; - I just seek to use a simple Old Latin as we do Old English, old chinese and old egyptian to make it easy.