self-rule vs self-government

self-rule and self-government both are nouns.

Word	Noun	Adjective	Verb	Adverb
self-rule	Yes	No	No	No
self-government	Yes	No	No	No

As nouns, self-rule and self-government are synonyms defined as:

self-rule and self-government: government of a political unit by its own people

Other synonyms of self-rule include self-determination.

self-rule (noun)	self-government (noun)
government of a political unit by its own people	government of a political unit by its own people