self-government vs self-rule

self-government and self-rule both are nouns.

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

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

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

Other synonyms of self-government include self-determination.

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