When we do \l+ , it is different than source, when we load backup from target server.
Backup is taken using pg_dump and its loaded as psql db name <backup>
It's normal that there is a size difference.
Basically you have a database you dump which may have many versions of visible rows or may have free space in the table, etc.
You take the most recent consistent backup of the visible data when you take a dump.
You create a database with only that information in it. So one generally expects it to be smaller. In for a db of reasonable size and load the difference may be 2x or more.
If you're talking about space on drive then you can expect the new one to be smaller generally as it has been straight efficient writes rather than a bunch of updates and deletes which create "holes" in the physical file space.
It helps if you are more detailed as to what you've observed if you want a more specific answer.
