calm > < quiet

Calm అంటే ప్రశాంతంగా. Quiet అంటే నిశ్శబ్దంగా.  Calm is used to talk about state of mind ie., without any emotion. Tranquil ఇంకా ఎక్కువ stage.
Quiet - silently without making any sound opp: noisy. 
 Eg. Stay calm in a crisis. Be quiet! The baby is sleeping.