Exit - is simply a way out. It refers more to a location in physical space (though not always). Can be a noun or a verb. Departure - is tells you more about the movement of leaving a place especially over a long distance. This is a noun from the verb "depart". Outing - is more about recreation. It implies that you'll be coming back after and usually on the same day. It's a noun only. Leave - is about going somewhere and not coming back. It's more final. Can be used as a noun, but sound better as a verb.

They're all very similar, EXCEPT for outing. "Outing" is used like "we had a company outing" aka "we had a company party/event." Exit is fairly technical - "Please exit the Zoom meeting." "The investor exited his investment in the company." "Please exit the movie theater using the door on the left." Departure is used for things like flying and travel, but not exclusively. "Our flight departs tomorrow morning." "Bilbo and Frodo departed for their final adventure." Leave is the most common for everyday use. "I left the party and went home." "He is leaving (resigning/quitting) the company tomorrow." "When I eat, I leave nothing on my plate." There's probably a better way to explain this but this is a start.

Hi, To exit, to depart, and to leave are all verbs meaning to move away from the place you are. ‘An outing’ is a formal way of saying going out somewhere (I.e. not at home). E.g. Shall we go on an outing this afternoon? Departure is usually used in conjunction with a time for public transport e.g. the train departs at 9:00. An exit can also be a noun, e.g. follow signs for the emergency exit (door). Hope this helps ☺️