/exit and /quit
/exit and /quit do exactly the same thing, with no difference in behavior between them whatsoever.
Both exist simply because either one is a natural word to reach for out of habit depending on what other tools you are used to, and tCode does not want an arbitrary choice between the two to be something you have to remember correctly under pressure.
There is no preferred one between them; use whichever comes to mind first in the moment.
Both also behave identically regardless of what state the session is in, mid-turn, waiting on a permission prompt, or idle at the prompt; either command ends the session cleanly from any of those states.
This is a small piece of polish rather than a significant design decision, but it reflects a broader pattern in how tCode's commands are chosen: favoring what a user would naturally reach for over insisting on one canonical spelling for the sake of it.