The exit is the door through which you can leave a public building.

An exit on a motorway or highway is a place where traffic can leave it.

If you refer to someone's exit, you are referring to the way that they left a room or building, or the fact that they left it.

If you refer to someone's exit, you are referring to the way that they left a situation or activity, or the fact that they left it.

If you exit from a room or building, you leave it.

If you exit a computer program or system, you stop running it.