Lots of differences, actually.
An email backup is a snapshot of a specific point in time, it’s purpose is for recovery in case of a disaster. Email archiving does not archive a series snapshots but it preserves all data history. The purpose of the archiver is much broader: discovery, compliance, legal, search, analysis and for regulatory and policy obligations.
For example: emails that have been sent or received and then deleted before the backup has been taken, are not available while they are present in the email archiver. Every email enters the email archiver in real time, as soon it is transmitted or received, and frozen there. Quite different from a snapshot.
While a backup data retention policy can only be based on age of data, the data retention policy of the email archiver is very flexible and can be based on age, content, metatada and legal-hold status.
There are also practical conveniences in using the archiver: emails can be automatically deleted from the mailserver in order to reduce it’s load. You can keep only one or two years of email in your mailserver, older emails are still are available on the archiver with even greater search speed and more flexibility of access: the Outlook plugin, the mobile apps, the web interface.
Basically, you can think at the backup as something for administrators while archiving is mostly for users.
As soon as an email is received by the archiver it is hashed, timestamped and certified (RFC3161) providing historicity and valid legal proof of existence and integrity. Whenever that email is retrieved the certified timestamp is verified. The validity of the certified timestamp can also be assessed by third parties using non-proprietary tools.
Full-text search on email content, attributes and metadata enables efficient discovery. Complex searches returning hundreds of thousands of items are performed typically within 0.1 seconds.
Retention periods can be optimized for different email categories: for example email pertaining the organization core business can have a different retention time than bulk email.
Legal hold allows preventing email related to legal cases from being deleted for any reason, until the specified period.
Summarizing: the email archiver provides much more than a backup: not a recovery tool in the hands of the administrators but a production and compliance tool for the whole company.