Do native speakers know the tenses?

Present simple, past continuous, future perfect, present perfect continuous etc.
These terms are used when English is taught to foreigners. All of them are from quite a neat chart 3×4 of tenses, which are studied thoroughly and separately, and then in speech.
I was wondering if native speakers students who study English use the same terms and approach. I got this idea after I'd read the book of English grammar, by British for the British. It is quite old, and maybe the approach is outdated too. It said there were two tenses, present and past. All the rest were just syntactical constructions for detailed meanings.