PostgreSQL - restored database smaller than original

The short answer is that database storage is more optimised for speed than space.

For instance, if you inserted 100 rows into a table, then deleted every row with an odd numbered ID, the DBMS could write out a new table with only 50 rows, but it's more efficient for it to simply mark the deleted rows as free space and reuse them when you next insert a row. Therefore the table takes up twice as much space as is currently needed.

Postgres's use of "MVCC", rather than locking, for transaction management makes this even more likely, since an UPDATE usually involves writing a new row to storage, then marking the old row deleted once no transactions are looking at it.

By dumping and restoring the database, you are recreating a DB without all this free space. This is essentially what the VACUUM FULL command does - it rewrites the current data into a new file, then deletes the old file.

There is an extension distributed with Postgres called pg_freespace which lets you examine some of this. e.g. you can list the main table size (not including indexes and columns stored in separate "TOAST" tables) and free space used by each table with the below:

Select oid::regclass::varchar as table,
      pg_size_pretty(pg_relation_size(oid)/1024 * 1024) As size,
      pg_size_pretty(sum(free)) As free
 From (
   Select c.oid,
       (pg_freespace(c.oid)).avail As free
     From pg_class c
     Join pg_namespace n on n.oid = c.relnamespace
    Where c.relkind = 'r'
      And n.nspname Not In ('information_schema', 'pg_catalog')
 ) tbl
 Group By oid
 Order By pg_relation_size(oid) Desc, sum(free) Desc;