I just want to check that my understanding of these two things is correct. If it's relevant, I am using Postgres 9.4.
I believe that one should vacuum a database when looking to reclaim space from the filesystem, e.g. periodically after deleting tables or large numbers of rows.
I believe that one should analyse a database after creating new indexes, or (periodically) after adding or deleting large numbers of rows from a table, so that the query planner can make good calls.
Does that sound right?
collects statistics and should be run as often as much data is dynamic (especially bulk inserts). It does not lock objects exclusive. It loads the system, but is worth of. It does not reduce the size of table, but marks scattered freed up place (Eg. deleted rows) for reuse.
reorganises the table by creating a copy of it and switching to it. This vacuum requires additional space to run, but reclaims all not used space of the object. Therefore it requires exclusive lock on the object (other sessions shall wait it to complete). Should be run as often as data is changed (deletes, updates) and when you can afford others to wait.
Both are very important on dynamic database