As far as I understand, both of these mean more or less the same thing. Duolingo, that introduced me to the Russian language seems to prefer учитель, but Russian Pod 101 prefers преподаватель.
Is преподаватель just more formal, or is there something more subtle going on?
"Преподаватель" is more often a professor in college or university, or instructor on some specific courses. While you can list (and consider) teachers in school as "преподаватели" the reverse is not true - nobody calls anyone "учитель" in system of higher education.
Also, "учитель" is uses for describing someone who is a spiritual teacher. Sort of like Yoda was for jedis or Splinter for teenage mutant ninja turtles ;)
Another subtle thing worth to mention, on can refer to somebody as "учитель" (like in phrase "Но учитель, как же мне тогда быть"), but referring to somebody as "преподаватель" sounds very unnatural to the native speaker. One will use the reference to position (like "Профессор, скажите пожалуйста") or just name ("Оксана Николаевна, можно задать вам вопрос?").
how would a native speaker refer to their university professor? As usual in Russian, by "name-patronymic" pair."Профессор" is quite rare (and is not appliable to associate professors and such). Also in student slang the word "преподаватель" is typically reduced to "препод" (not suitable for communicating with profs, of course).
I believe, both преподаватель and учитель are positions:
учитель - at school, преподаватель - at university, professional courses etc.
Also учитель has another meaning: mentor.
