Is Aghadown, Cork, Ireland and Aughadown, Cork, Ireland two different parishes?

Aghadown is the name of  a civil parish in Co. Cork, the corresponding Catholic Parish is oftern referred to as Aughadown or sometines Aghadown or the "Union of Aughadown". The Catholic parish of Aughadown also covered two other adjacent civil parises i.e. Abbeystrowry and Kilcoe.

Older references to the civil parish can use 'Aughadown' as the spelling so depending on the context Aghadown/Aughadown could be a reference to either the Civil or Catholic parish.

see the entry in Lewis Topographical Dictionary 1837 Aughadown (LibraryIreland.com)