Yes, there is a difference. Schüler (der Schüler, die Schülerin) is for a school student - that would cover K-12 (in US terms). Student (der Student, die Studentin) is for a college / university student
That's right. Technically, it's K-12 minus the K. Kids attending kindergarten are not called "Schüler", but "Kindergartenkinder".
So would "Wir sind drei kleine Schülerinnen" be an accurate (if unpoetic) translation of "Three little maids from school are we"? Whereas I couldn't use Studentinnen? Unless they were attending the University of Titipu?
der Student = male student
die Studenten = male students
die Studentin = female student
die Studentinnen = female students
In German, it's mandatory to specify the gender. For students in general or mixed groups, use the masculine form.