Love those comparisons...
POP3 does not provide access to server side folders. Period.
Even a mail app called "My" (or "Your"... or "Gold Email Platinum Plus Pro") won't be able to access folders over POP3, there is no magic.
If another mail app is able to access your actual server folders, it must be using something other than POP3.
If your mail provider is the company providing your Internet connectivity -- apparently they rolled out IMAP recently, but I wasn't aware of it so the preset in Aqua still uses POP3.
Please remove the account from Aqua and add back using Manual account setup mode (you'll see Manual button after entering your email + password) -- and change the server type and server from POP3 to IMAP.
Your mail provider's IMAP settings are easy to find in Google web search (not posting here, protecting your privacy).