rebellion vs insurgency

rebellion and insurgency both are nouns.

Word	Noun	Adjective	Verb	Adverb
rebellion	Yes	No	No	No
insurgency	Yes	No	No	No

As nouns, insurgency is a hyponym of rebellion; that is, insurgency is a word with a more specific, narrower meaning than rebellion:

rebellion: organized opposition to authority; a conflict in which one faction tries to wrest control from another
insurgency: an organized rebellion aimed at overthrowing a constituted government through the use of subversion and armed conflict

Other hyponyms of rebellion include insurgence, intifada, intifadah, mutiny.

rebellion (noun)	insurgency (noun)
organized opposition to authority; a conflict in which one faction tries to wrest control from another	an organized rebellion aimed at overthrowing a constituted government through the use of subversion and armed conflict
refusal to accept some authority or code or convention