public house vs gin mill

public house and gin mill both are nouns.

Word	Noun	Adjective	Verb	Adverb
public house	Yes	No	No	No
gin mill	Yes	No	No	No

As nouns, public house and gin mill are synonyms defined as:

public house and gin mill: tavern consisting of a building with a bar and public rooms; often provides light meals

Other synonyms of public house include pothouse, pub, saloon, taphouse.

public house (noun)	gin mill (noun)
tavern consisting of a building with a bar and public rooms; often provides light meals	tavern consisting of a building with a bar and public rooms; often provides light meals