public assistance vs aid

public assistance and aid both are nouns.

Word	Noun	Adjective	Verb	Adverb
public assistance	Yes	No	No	No
aid	Yes	No	Yes	No

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

public assistance: governmental provision of economic assistance to persons in need
aid: gift of money or other material help to support a person or cause

Other hypernyms of public assistance include assistance, economic aid, economic assistance, financial aid, financial assistance.

public assistance (noun)	aid (noun)
governmental provision of economic assistance to persons in need	the activity of contributing to the fulfillment of a need or furtherance of an effort or purpose
	the work of providing treatment for or attending to someone or something
	a person or thing that is a resource that helps make something easier or possible to do
	gift of money or other material help to support a person or cause

public assistance (verb)	aid (verb)
	improve the condition of
	give help or assistance; be of service