I've had two Japanese professors so far, and they have both split verbs into two groups for teaching English-speakers: they call godan verbs u-verbs and ichidan verbs ru-verbs. I never really liked these terms because, for one thing, a verb can end in -ru without being a -ru verb. The groups just seemed inconsistent, even though I knew what they were meant to represent. I always knew the verbs by godan, kami-ichidan, and shimo-ichidan because I came across the terms on my own. Do native Japanese speakers refer to verbs exclusively as godan/ichidan, or are those terms basically only known by linguists while most people use some other term to describe them? Is that how they are taught in schools/would any given native speaker know those terms?
I'm from Japan and received Japanese education for 14 years. Yes. I think I remember being taught godan katsuyo as basic Japanese grammar class in elementary school -- around 5th or 6th grade. I don't remember ichidan, but when I did a quick Google search, I found many articles about that and reminded me it was a part of grammar we were taught. goadn katsuyo is probably well known among most of Japanese who completed at least 9 years education which should be 100%. But the rest may be forgotten. Like you said, unless you are linguists or Japanese language-major students, we hardly care about how our language should be explained.