If I want to invite my school’s superindentent to Common App to write a recommendation letter for me, do I invite him/her as a teacher or “other recommender”?
If he/she has never been your teacher, then invite under “under recommender.” My D17 did exactly this upon the advice of her high school’s college counselor.
Superintendent’s recommendation letter falls under “other recommender.” Think of it as getting a recommendation letter from your football coach, who is part of your school faculty but is not a teacher who grades you or whose judgment doesn’t factor into your school grade.