The database backup sizes listed in the Site Backup & Restore tool appear different after exported.
MySQL is a complex relational database that can contain extremely vast amounts of information—and can also store that information in a number of different ways, for efficient querying. Because of this, when a database is “live”, it's size is typically much larger.
When "live", the database will be split up into a number of separate files, with control structures, coding and other information necessary for the database to operate properly.
When exporting to an SQL file, the structures are removed and only the database data is kept, hence the typically much smaller size.