Syncing iPhone Apple Mail With MacBook Apple Mail App

Mail is an app. It is an app that provides interaction with an email server. That email server can host one of various email protocols. Mail is not an email provider. It is just a client that talks to an email provider and collects your email messages from the provider. Your email provider will be the part of your email address after the @.

There are several protocols an email provider can use to host your email service. The only one that doesn’t “sync” is the post office protocol, POP.

You must not be using the POP protocol in order to have your email “sync” across devices.

On the protocols that “sync,” all of the information is stored on the server so when you connect with a different device, you will see the same information. Nothing is really sync’d. You just view the server data from a different device.

The fact that you think Mail is your email provider likely means you are using iCloud email which is IMAP and should appear the same on all devices.

On Mail on macOS you can create mailboxes (folders) in a section titled, On My Mac. Those will never sync with Mail on your iPhone. If you create the mailboxes on the email provider’s server, you will see them on all devices. In Mail, you create a mailbox on the server by choosing that account in the popup menu on the New Mailbox dialog.

Just using the standard email app on my Iphone - wanting to synch it to the standard email app on my MacBook... so folders & emails are shared & updated automatically.... This doesn't seem like mismatch of email providers...

The app has nothing to do with it. An email provider, like iCloud, provides you with an email address.

You set up that account in an email client like Mail. If you are using iCloud, then the two should sync.

There are two internet email protocols, POP and IMAP. POP will not sync. iCloud is IMAP and will sync.

The folders must reside on the email server. If you created On My Mac mailboxes and moved messages into those, they will never sync.

You need to use a server-based email provider (e.g., IMAP, Exchange). What email provider are you using?