rejoicing vs exulting

rejoicing is a noun but exulting is not a noun.

Word	Noun	Adjective	Verb	Adverb
rejoicing	Yes	Yes	No	No
exulting	No	Yes	No	No

As adjectives, rejoicing and exulting are synonyms defined as:

rejoicing and exulting: joyful and proud especially because of triumph or success

Other synonyms of rejoicing include exultant, jubilant, prideful, triumphal, triumphant.

rejoicing (noun)	exulting (noun)
the utterance of sounds expressing great joy
a feeling of great happiness

rejoicing (adjective)	exulting (adjective)
joyful and proud especially because of triumph or success	joyful and proud especially because of triumph or success