A dictionary of Confusable Phrases: More Than 10,000 Idioms and Collocations

public house • public housing
public house —a licensed saloon or bar: Both these sorts of
public house are essentially working class; the blackcoat’s pub
is another sort of place.
Note: 
a) The expression is not equivalent in meaning to the
phrase public bar—(UK) a drinking room in a pub where drinks
are sold at the counter, as contrasted with a “saloon bar” or
“lounge bar” where tables are provided and drinks are brought
by waiters: Pubs usually have two separate rooms; first, public
bar which is in general frequented more by men … second,
lounge bar in which there is more equal number of men and
women.
b) The expression does not correlate in meaning with the phrase
public home
— a communal building: There are a number of
hospitals, asylums and public homes, including ten public
hospitals, the largest of which is the Toronto General hospi-
tal.
public housing —low-rent dwellings owned or administered
by a government: When federal officials hoped to proceed to
more substantial matters such as public housing and public
assistance, the states turned balky.
public school (UK) • public school (U.S.)
public school (UK)—prestigious fee-paying independent sec-
ondary school, usually boarding: They called that kind of
school a public school, which in England was the name for a
private school which your parents have to pay quite a lot of
money to send you to.
public school (U.S.)—non-fee-paying school supported by
public funds and controlled by a local governmental authority:
The rates have been lowered and the town people had been
wooed to send their sons to Gilford instead of to public school.
See also: private school (UK) / private school (U.S.).