on the spur of the moment vs of a sudden

on the spur of the moment and of a sudden both are adverbs.

Word	Noun	Adjective	Verb	Adverb
on the spur of the moment	No	No	No	Yes
of a sudden	No	No	No	Yes

As adverbs, on the spur of the moment and of a sudden are synonyms defined as:

on the spur of the moment and of a sudden: quickly and without warning
on the spur of the moment and of a sudden: happening unexpectedly
on the spur of the moment and of a sudden: on impulse; without premeditation

Other synonyms of on the spur of the moment include abruptly, all of a sudden, dead, short, suddenly.

on the spur of the moment (adverb)	of a sudden (adverb)
quickly and without warning; happening unexpectedly; on impulse; without premeditation	quickly and without warning; happening unexpectedly; on impulse; without premeditation