For regular users they click the Trash icon to flag a record for deleting. The privileged users can then view the contents of the Trash and delete those icons.
Delete is permanent, where as Trash can be thought of as a location.
The user can move records to the Trash.
and
The privileged user deleted records in the Trash.
The other words don't work well for me.
I don't like Recycle because it implies a different meaning then simply deleting records.
Archive implies permanent storage, and possibly moving the records to offline storage.