free house vs public house

free house and public house both are nouns.

Word	Noun	Adjective	Verb	Adverb
free house	Yes	No	No	No
public house	Yes	No	No	No

As nouns, public house is a hypernym of free house; that is, public house is a word with a broader meaning than free house:

free house: a public house that is not controlled by a brewery and so is free to sell different brands of beer and ale
public house: tavern consisting of a building with a bar and public rooms; often provides light meals

Other hypernyms of free house include gin mill, pothouse, pub, saloon, taphouse.

free house (noun)	public house (noun)
a public house that is not controlled by a brewery and so is free to sell different brands of beer and ale	tavern consisting of a building with a bar and public rooms; often provides light meals