I left the fireteam in Destiny in the tower but did not leave the chat, even when I switched to a different game! I felt dumb because I did not know how to exit the chat so I muted the mic but then was the subject of discussion. (awkward!) How did I leave the fireteam but not the chat? Was the chat somehow console (PS4) managed instead of destiny/bungie managed?
It sounds like you joined a Party Chat. This is a feature of the PS4 that allows people to communicate even when they aren't in the same game.
To leave the party chat: