basically Anna teamed up with Foley in 1999 and created the Foley + Corinna, however, it seems as though some of the bags (with the same designs) are under the Anna Corinna label. I don't think there is a quality difference in the bags.
My guess is:
They initially produced bags ONLY under the 'Anna Corinna' name, and than tried to phase them out with new 'Foley+Corinna' labels. However, the Anna Corinna bags are still all over the place.
Nope, there aren't! As far as I can tell, Dana Foley designs the clothes produced by Foley + Corinna, whilst Anna Corinna designs the bags produced under the label. Hence, Anna Corinna's bags that were under the Anna Corinna label "live on" as Foley + Corinna bags today (e.g. the City tote, Jet Setter Jr tote).