My personal opinion is that both come from the original Greek root words, "an" and "archos." "An" means without, and "archos: refers to rulers. So just "without rulers." Therefore, in my mind, any bit of baggage that gets added to the definition along the way is merely connotation.
But I can see why you might see personal differences between the two. In either case, thank you for posting on my wall and following my posts.