Random question here. Is μαθητής more of a younger, as in gradeschool, student? Or would I (age 40) use this word as well?
A college student is φοιτητής, a primary or secondary education student is μαθητής but there is no age connotation.
A learner is a person who learns: for example we are all learners in DL but since we don't have any teachers we are not students. The word "μαθητής", as it is used in modern Greek, specifically implies that there is a teacher involved in the learning process.