If I look at Folders, all my accounts (GMail and otherwise) have five options: Inbox; Sent mail; Drafts; Spam; Trash. IMAP accounts also have Archive. In every case, all of those folders can be defined.
The other thing to check is to be sure you’re hitting Delete and not Archive when you get rid of your emails! I’ve found myself doing the wrong one before now and it leads to much confusion. (Whoever invented the Archive concept just made life hugely harder for everyone IMO!)