What is the difference in Mail between Inbox and All Mail?

You use GMail, and All Mail is a special GMail mailbox. When you delete a message from a GMail account, it's supposed to stay in the All Mail mailbox forever, so you can still find and refer to it if necessary at some future date.

If you don't like the All Mail mailbox, just hide it from Mail so you don't have to see it.

Hiding GMail’s “All Mail” from Apple Mail

It's only an invasion of privacy if Google goes snooping in there, which there's no evidence to suggest that they are doing. You can manually remove messages from the All Mail folder via the web-based GMail interface if you like. If you feel strongly that mail should be permanently removed from the server when you delete it, though, GMail is not the service for you.

From a discussion a while back:

You can make settings at the gmail site to where it does exactly what you do on your Mac. You can hide the All Mail folder in IMAP as Thomas suggested. Messages won't stay in it when you delete them from the Mac.

The All Mail Folder will show messages no matter what folder they are in. GMail's default settings would keep the messages deleted in a Deleted Items folder rather than sending them directly to the trash. It's been a while since I had a gmail account, but the settings should be close to the same.

Just make sure the Trash and Sent Messages imap mailboxes are mapped correctly to Mail's main mailboxes and mailbox behaviors are set to store messages on the server.

Discussion here:

https://discussions.apple.com/thread/4046130?answerId=18944014022#18944014022

Affricat,

Go to your Gmail account, delete the files in All Mail. As for invasion of privacy, have you read the Gmail TOS? You may be surprised.

Mail goes from sender to you through server after server. Usually when it reaches its destination it does not reside on ones computer it is on a server someplace. Unless the mail is encrypted do not think of it as private, it is stored in plain text someplace.

Also, remember your phone, when turned on, always knows where you are. Your bank and credit card company knows your spending habits, many cities have surveillance cameras, the list goes on. So, your comment "...quite an invasion of privacy...", repectfully is without merit.

Cordially,

RicD

I've heard the only way your phone isn't able to track you is if you remove the battery -- impossible on an iPhone.

There's nobody tracking you through your phone, that's conspiracy theory nonsense. Why would anyone you don't know be interested in knowing where you are, unless you have done something highly illegal to warrant having your activity monitored by a law enforcement agency?