Please, read FAQ "How do I access server side folders?":
http://www.aqua-mail.com/?page_id=227Unless you configured any messages sorting/filtering, by default, in Gmail you have all incoming messages in the INBOX, and then additionally most (or all?) messages are assigned a label for the categories you described. Those labels will appear as folders in Aquamail and you can configure them to be synced. But the same messages would appear in the "All Mail" Incoming folder(mailbox).
Note that deleting a message from, say, "Social" folder would not delete that message from "All Mail" (Inbox) folder.
One possible solution to that could be to configure only the "sorted" folders to sync, while disabling sync for "All Mail".
I think that scenario should work, - but I have never tested all details of it. In particular, I am not sure if there could be situations when
no additional label is assigned for a message by Gmail (with the default settings).