Vacuum in postgresql and Purge in mysql
Similar, but not exactly.

They are both related to the MVCC architecture, and related to garbage collection, broadly speaking.

Vacuum in PostgreSQL removes obsolete or deleted record versions, and marks the space as available for re-use. This is accomplished by running the VACUUM command periodically, or by enabling the optional autovacuum daemon.

Purge in MySQL removes obsolete InnoDB record versions from the rollback segment, so that space becomes available for re-use. Purging happens automatically every 10 seconds in the InnoDB server master thread, or in a dedicated purge thread. In fact, you can't disable purging unless you run MySQL in a forced-recovery mode.

The difference is subtle and related to the respective implementation of MVCC. Probably the answer you're looking for is simply, yes.