This is for the state of Texas only. Texas statutes answer that question, very well, for members in State Statute 209.002, item 7 (Link is –> Here) :
(7) “Property owners’ association” or “association” means an incorporated or unincorporated association that:
(A) is designated as the representative of the owners of property in a residential subdivision;
(B) has a membership primarily consisting of the owners of the property covered by the dedicatory instrument for the residential subdivision; and
(C) manages or regulates the residential subdivision for the benefit of the owners of property in the residential subdivision.
It is answered, once again, in statute 211.001, item 3 (Link is –> Here) :
(3) “Property owners’ association” means an incorporated or unincorporated association owned by or whose members consist primarily of the owners of the property covered by the dedicatory instrument and through which the owners, or the board of directors or similar governing body, manage or regulate the residential subdivision or similar planned development.