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The key difference is that a mailbox is a digital storage space for emails—like a physical mailbox—where you receive, manage, and send messages.
An email alias, on the other hand, is an alternative or additional email address linked to an existing mailbox. It has no storage or login of its own; emails sent to an alias are delivered directly to the inbox of the connected mailbox.

Email alias

If you’d like to use a separate address for things like online orders or financial matters, it’s best to create an aliasaddress. You can use this alias, for example, when placing an online order.

Want to keep those emails in a separate folder? You can set up an email filter to organize them automatically—without needing to create a second mailbox.

📄  Learn how to create an alias in the Add an alias article
📄  Learn how to set up filters in the Email rules & moving messages to folders article

Mailbox 

A single main account can include multiple mailboxes. While mailbox management happens via the main account, only the mailbox owner (and thus the owner of that email address) has access to its content. Each mailbox is linked to a domain, and you can create multiple mailboxes under the same domain.

Need to give other people access to a specific mailbox or email account? You can do this by logging in on multiple devices using device-specific passwords.

📄  Learn how to Create a device-specific password