The ANA is the American Numismatic Association, a non-profit Congessionally chartered national coin club which publishes the Numismatist and allows members to borrow from its a superb library of numismatic material, among other things. NGC is the Numismatic Guaranty Corporation, is a commercial corporation engaged in the business of cetifying its opinion as to the grade and authenticity of collectible coins, and seals them in (hopefully) tamper proof plastic packaging, generally referred to as "slabs".
NGC is the official grading service of the ANA. If you are an active member of the American Numismatic Association (ANA), you may submit coins directly to NGC for grading. Other wise you have to join NGC's collector club which is $99.00 per year or have an authorized dealer send them for you. Hope this helps. Ed
ANA is a club, as you have already heard, perhaps you are referring to ANACS, a third party grading service (TPG). If so, then NGC is considered one of the top two services, along with PCGS, although PCGS considers them no competition. ANACS comes in third, but, with the recent change in management and location, there has been some debate about the future of the service. Frank