The Latin that students read in Latin class is what's called "Classical Latin," although it should more accurately be termed "literary Latin." It is not the spoken form of the language, it is a highly artificial literary construction. Nobody spoke the way that Cicero does in his speeches--indeed, not even Cicero did, since many of his letters use a decidedly different (though still very educated) form of the language. The spoken form of the language was what is called Vulgar Latin. "Vulgar" here does not mean obscene, it means "common"--Vulgar Latin was the normal form of the language. Like every colloquial form of speech, there is no single Vulgar Latin--I discuss that here. The way I speak conversationally will differ from the way you speak, based on our relative levels of education, regional differences, whether the language we're speaking in is my native language or yours (or neither of ours), our upbringings, our relative status (you're not gonna say "sup dog" to a college professor), and simply our personalities. Latin is no different. The high literary style of Classical Latin would not have been used in any actual colloquial speech by any group of society, but what Cicero might have considered conversational speech is very different from what a provincial would have thought--another thread in which I speak of this is here. Vulgar Latin idioms permeate throughout our corpus of Latin. Besides literary works in which these idioms are used (which is literally every literary work in Latin ever, since you can't write even an artificial literary form of the language without some colloquial idioms sneaking in, that's the way language works--Silver Latin authors and Ciceronian prose, however, often intentionally attempts to insert vulgar idioms into their prose for stylistic purposes) we have graffiti, certain inscriptions, etc. Vulgar Latin differs depending on who's speaking, where they are, and when they're writing, as has been said, but most forms of colloquial Latin speech are characterized by the dropping of certain cases or their misuse, the abuse of prepositions, the simplification of conditional clauses, and quite a lot of very idiomatic phrases (particularly connectives--Cicero especially likes to use idiomatic colloquial connectives in a very literary, logical way), and the general simplification of syntax. Many forms of Vulgar Latin use words in ways that are not their "dictionary" definitions--quite a lot of slang words for sexual intercourse are words for thrusting or beating being misused colloquially, for example. Provincial Latin is even weirder, since it often features vast changes to the language's structure and incorporation sometimes of local linguistic traditions. It's from Vulgar Latin (naturally, since it's the spoken language) from which Romance languages derive, and words like "cheval" in French point to idiomatic usages--"cheval" derives from Latin caballus, which means a nag or generally a shitty horse in literary Latin, but which appears to have been a common colloquial term for a horse in general in the provinces