public security vs security

public security and security both are nouns.

Word	Noun	Adjective	Verb	Adverb
public security	Yes	No	No	No
security	Yes	No	No	No

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

public security (noun)	security (noun)
the general security of public places	measures taken as a precaution against theft or espionage or sabotage etc.
	an electrical device that sets off an alarm when someone tries to break in
	a guarantee that an obligation will be met
	freedom from anxiety or fear
	a department responsible for the security of the institution's property and workers
	property that your creditor can claim in case you default on your obligation
	defense against financial failure; financial independence
	a formal declaration that documents a fact of relevance to finance and investment; the holder has a right to receive interest or dividends
	the state of being free from danger or injury