This question is similar to your last post asking the difference between officers and directors. Let me try and answer it this way:
HOA = Homeowners Association
COA = Condominium Owners Association
Association = general term for either an HOA or a COA
Typically, an Association is the corporation created to oversee the common area and enforce the governing documents. The members of the Association are the owners of the individual lots/units that must comply with the governing documents per the deed restrictions of that lot/unit.
As a corporation, the Association must comply with State corporate laws. These laws typically require that the Association be ran by an executive board or Board of Directors.
A sponsor of this site, Community Association Network, has made some great videos that might help explain it better. Here are the links:
Videos for Owners in Associations Videos for Board members Another site, HOA-USA has some good resources as well:
Georgia State Laws HOA-USA Georgia Resource Center Hope this helps,
Tim