“Pupil” or “Student”, what is the correct use?

I am from the United States and work in the public schools. It’s my experience that people attending school at all grade school are by far most typically referred to as “students,” rather than “pupils,” both in conversation and in writing. I have met non-native speakers who find it disconcerting that we use the same word for first-graders as college students, but it is the standard word to use, at least in the U.S. As one example, the school standards for the state of Minnesota refer to “students” throughout, regardless of age. For instance:

“The grades K–5 standards on the following pages define what students
should understand and be able to do by the end of each grade.” (K-5 means kindergarten through 5th grade, ages five to eleven or so.)

You can also just refer to them as “kids” or “children,” if the school context is already there. If you know the specific grade, you can say “first graders,” “second graders,” etc. “Pupils” in any context is more unusual and sounds more old-fashioned.

If you’re interested, the Minnesota K-12 Academic Standards in English Language Arts are available for download at http://education.state.mn.us/MDE/EdExc/StanCurri/K-12AcademicStandards/index.htm.