Formality or plurality.
Verb is "kalmak" (to stay/remain)
kal is the imperative command form for SINGULAR INFORMAL you. kalın is the imperative command form for PLURAL or SINGULAR FORMAL you.:) (So either form is saying "Be/stay well!")
Saying goodbye to one close friend or someone younger than you: Hoşça kal!
Saying goodbye to an elder or a boss: Hoşça kalın!
(A tad informal for a parting to a superior, but maybe you like your boss, I dunno.)
Saying goodbye to a group of folks: Hoşça kalın!
Okay so I'm not completely fluent in turkish yet so correct me if I'm wrong; But from the books I've studied I learned that when two people are parting, Hoşça kal (being singular and informal while Hoşçakalın is the plural,formal form) is used by the person who is leaving. güle güle on the other hand, is used when you are the person staying behind.