How is Studentinnen different than Studenten?
Studentinnen refers to female students, Studenten refers to male students.
I think if it is a mixed group, you use studenten, but I am not 100% sure on this.
Right on. There's also the gender-neutral "Studierende" which is pretty much only used by university administrations.
doesn't Student mean (university) student and Schuler mean (school) pupil?
Is there a reason that even though "students" in English could translate into either "Studenten" or "Schulerinnen" it won't usually accept both?