exit vs log off

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

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

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

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

exit (verb)	log off (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