mouth off vs rant

mouth off is not a noun while rant is a noun.

Word	Noun	Adjective	Verb	Adverb
mouth off	No	No	Yes	No
rant	Yes	No	Yes	No

As verbs, mouth off and rant are synonyms defined as:

Other synonyms of mouth off include jabber, rabbit on, rave, spout.

mouth off (noun)	rant (noun)
	pompous or pretentious talk or writing
	a loud bombastic declamation expressed with strong emotion

mouth off (verb)	rant (verb)
talk in a noisy, excited, or declamatory manner	talk in a noisy, excited, or declamatory manner