In usa, Student= student of any kind. A person actively going to school classrooms in any school to or a person being taught by another person whether a private tutor/teacher or even your own mother= student. the teacher can be anybody. it does not have to be an official teacher and you dont have to be an official student. for example, if you go into the mountains and are learning kung fu from a hermit, you would be his student and he would be your teacher. College/university - too long to get into - you can call all college or university( yes, there's a usa difference) students "college students", but if a student is enrolled in a 2-year long post-grade school educational institution, known as a "college", and most will literally have "college" in their title(their name), like west los angeles college or Los angeles city college, then they cannot be accurately described as a university student. These colleges can be used to complete the first 2 years of the 4 years we spend in university in usa. And you cannot get a Bachelors degree, a 4-year degree, in a college like the examples i gave. Inside universities, their schools for different subjects are sometimes called "college of engineering" or "college of arts", but I am not talking about schools within universities so dont get confused by that.
male: der Student, die Studenten // female: die Studentin, die Studentinnen
For university students of both genders, it used to be common to use die Studenten as a generic plural; however, it's common these days to see die Studierenden (inflects like an adjective, e.g. Studierende without an article before it) as a gender-neutral plural. That literally means "(people who are) studying".
male: der Schüler, die Schüler // female: die Schülerin, die Schülerinnen
I don't know of a commonly-used truly gender-neutral plural here; using die Schüler is probably the best way to go here unless you use die Schulkinder "the schoolchildren".