One must be careful; the Latin you might have learned in school is not the Latin your everyday Roman spoke. It was a poetic Latin hugely influenced by Cicero, whose rhetoric is seen as the peak of written Latin. Your everyday Latin to any time of the Roman empire was way "easier", less structured and complex in Syntax and vocabulary.

Vatican Latin is going a middle way. We call it Church Latin, a Latin, which shows strong influences of the classical Latin of Cicero, Caesar and co. but also influences of modern day Italian in the way it is spoken or vulgar Latin and written Latin of the middle ages and late antiquity.

Church Latin is not the same as the classical Latin in the tradition of Cicero, but it has many similarities.

Summarized one could say: It is not the Latin the Romans spoke, but shares many similarities with the Latin of Cicero taught in schools up to this very day.

This kind of strikes at the definition of what the difference between a language and a dialect, and the ways languages evolve over the course of time. There is no universal linguistic differentiation of language versus dialect, but one of the major things would have to be intelligibility - would native speakers of one language be able to understand the other?

This, however, is complicated by the development of language. We call Old English Old English because it was a foundation part of the development of modern English. Same with Middle English. If you're not familiar with Middle English, hearing it spoken would be nearly unintelligible - but you can pick up Chaucer and be able to decipher a large amount of it without any specialized training. Are both languages English? What about Old English, which would be more intelligible to a modern German-speaker than to a modern English speaker?

To see what I mean, listen (don't read) the link here: https://www.youtube.com/watch?v=QE0MtENfOMU

Then read the same text: http://www.librarius.com/cantales.htm ^1

You'll be able to understand much more by reading than by listening.

The vocabulary of Classical and Church Latin are very similar - obviously Ecclesiastical Latin has some specialized language that Classical Latin would not. The pronunciation has several important distinctions - Ecclesiastical Latin includes soft Cs, lengthens all of the vowels, uses the "v" sound (in Classical Latin "v" made a "w" sound).^2, 3 There are also some other differences in pronunciations of diphthongs. Ecclesiastical Latin also has simpler lexicon compared to classical Latin.^4

What I would say is that it is a remarkably similar language giving the gulf of time that divides them. In the time between the birth of Christ and now Classical Latin has naturally morphed into Italian, Portuguese, French, Spanish etc. These are now fully independent languages with shared roots but vastly different spelling, etc. The pronunciation changes that have occurred to Church Latin over that same period are much, much smaller, smaller even than the changes between Middle English of Chaucer's day and Modern English.

Given the similarity I think we can safely say that Ecclesiastical Latin is the only currently existing form of the Latin Language, and that, though it has evolved and morphed over time, it has done so remarkably little, and would be intelligible by an ancient Latin reader, and somewhat intelligible by a listener.

Fun side note:

Arabic is an interesting case study of a similar phenomenon. Arabic first spread across Northern Africa to Iran from c.600-c.750. The language written and spoken at the time is Classical Arabic - a language that is still in use as a standard language across the Arabic world. This is the language of the Koran, but also the language used in newscasts, even though no one learns it natively (somewhat like acquired pronunciation in England).^5 Arabic has, since 750, been splitting into different dialects, especially vis. pronunciation. Most are mostly mutually intelligible, and classical Arabic is intelligible to all of the dialects. It will be interesting to see if this process of splitting continues, or if mass media brings more and more speakers towards classical Arabic - or maybe they all meet somewhere in the middle.

Sources

1. Chaucer. Canterbury Tales. 1478.

2. Wheelock, Frederick M. Wheelock's Latin, 7th edition. Revised by Richard Lafleur. 2011 xxxv.

3. Collins, John F. A Primer of Ecclesiastical Latin. 4.

4. Ibid.

5. Brustrad, Kristen. Alif Baa. Georgetown University Press, 2008. 8.