Difference between database backup and data-tier application export
A backup is a full copy of all the database pages, or a dump of the database if you like, starting at page 0 and written sequentially to the backup device.

The Data-Tier application is a set of scripts that will create the database objects along with insert statements that will insert the data into the table objects afterwards.

From a backup perspective the Data-Tier application is a snapshot of the database in a certain state, you can install the application in that state but you can not restore additional data but have to copy the data from another source. The backup is a consistent state of the database and you can make log or differential backups that you can use to restore the database to a point in time.