Latin has changed through history, obviously, and many times the correct answer to a question is going to depend on which era the OP is talking about. What are the right high-level tags to describe the various major eras of Latin?
The following, primarily from Wikipedia, is now live on tag wikis of each era:
The primary eras of Latin, with approximate dates, are:
- Old (before 75 BC) old-latin
- Classical (75 BC to AD 300) classical-latin
- Late (300–500) late-latin
- Medieval (500–1400) medieval-latin
- New/Modern (1400–1900) new-latin
- Contemporary (1900–present) contemporary-latin
For the spoken Latin of the common people until the 6th century, use vulgar-latin.
For changes in Latin within and especially across eras, use language-evolution.
There is a major oversight here. Between Old and Medieval Latin, there existed spoken Latin. Scholars are pretty clear than the language of Cicero and Caesar or, conversely, Seneca and Quintilian were of a written style we call Classical, but that's not what the common people spoke. The common Latin, called vulgar (from sermo vulgaris) or colloquial, is not a regional variation of the Latinity of the orators, but was the lived language and was concurrent with the literary style.
While many will probably come here because of questions of literary Latin (in fact, the overwhelming majority will), surely some will come here for spoken Latin of the Republic and early Principate, and already some questions have been asked about the Vulgate (guess how it got its name!). With that, I propose vulgar-latin, with the initial date left off (so, "spoken Latin until the sixth century").