From what I’ve read, Anonna only exists in the real world. Freddy can exist in both real and dream worlds. Freddy can control and manipulate dreams, but Anonna can eat them. Annona has powerful psychic powers but Freddy is a completely insane psycho ghost who can turn himself into a snake and stretch his tongue and transform beds into trans-dimensional portals and turn you into a rubber mannequin and pull you through a 12x16 door window and can make his arms look like Slinky toys.
(btw, if I got anything wrong on Annona, please correct me, cos I know next to nothing about her)