community service vs public service

community service and public service both are nouns.

Word	Noun	Adjective	Verb	Adverb
community service	Yes	No	No	No
public service	Yes	No	No	No

As nouns, community service and public service are synonyms defined as:

community service and public service: a service that is performed for the benefit of the public or its institutions

community service (noun)	public service (noun)
an unpaid service for the benefit of the public that is performed by lawbreakers as part (or all) of their sentence	employment within a government system (especially in the civil service)
a service that is performed for the benefit of the public or its institutions	a service that is performed for the benefit of the public or its institutions