Translation:Some students are eating apples and the others do not eat apples.
If you break the sentence apart: 1) Des élèves mangent des pommes = (Some) students eat (are eating) apples (not "the apples") Ref the partitive "des" for plural countable things: http://french.about.com/od/grammar/a/de-vs-du-de-la-des_2.htm
The second phrase has to do with "the others" who "ne mangent pas de pommes" does not use the partitive, so they "do not eat apples" and not that they "are not eating (some) apples."
"élève" goes from "école primaire" (primary school) to "lycée" (high school), so basically from 6 to 18. After that we rather use "étudiant". But the difference is not that clear, because "élève" can simply designate someone learning from someone else, no matter the context, so even adults can be called "élèves", it's not a problem.
Both "pupil" and "student" can mean "élève", but only "student" can mean "étudiant".
Is this meant to be a general statement? I am particularly referring to "les autres" here.
I mean, "Some students [whatever] and others don't" would be a common way, in English, of expressing a general statement.
To say, "Some students do and the others don't" indicates we are talking about a particular group of students, not just students in general.
So - is "les autres" just how it's done in French, or would one say, perhaps, "des autres" for the more general remark?