"BE QUIET" means "SEI STILL" or "SEI RUHIG, (JETZT)" probably a teacher would say so if his student are chatting too much, besides "SEI STILL" is only used to address one single student...
or if ur friend doesnt stop talking and u need a short break... but then u should use a more polite form like "OK STOP MAL ICH BRAUCH EINE KURZE PAUSE UM MEINE GEDANKEN ZU SAMMELN!" (thats what i would tell them)
"SILENCE PLEASE" means "RUHE BITTE" or "RUHE JETZT" (thats how i suggest translating it) so the teacher would use it in case all of his students are chatting the whole time, so all pupils are spoken to stop their disrespectful behaviour...