exit vs log out

exit is a noun but log out is not a noun.

Word	Noun	Adjective	Verb	Adverb
exit	Yes	No	Yes	No
log out	No	No	Yes	No

As verbs, log out is a hyponym of exit; that is, log out is a word with a more specific, narrower meaning than exit:

exit (noun)	log out (noun)
the act of going out
an opening that permits escape or release
euphemistic expressions for death

exit (verb)	log out (verb)
pass from physical life and lose all bodily attributes and functions necessary to sustain life	exit a computer
lose the lead
move out of or depart from