Yeah, it's for National Association. To simplify even more, just remember, if you want to start a bank, you gotta register it either as a state bank or a federal one. If you go the latter route, you will be a N.A.
But as pointed out by Oski, that's only the tip of the iceberg. There's actually another layer of regulatory framework on top of the ones quoted above, as the Fed also regulates financial and bank holding companies. Anyway, it's a fascinating history how the US financial system came into place and anyone interested in economics or law should definitely look into it.