How to identify a parish

Hi...I dug up my great-grandfather's baptistimal record (https://registers.nli.ie/registers/vtls000634139#page/4/mode/1up).

My question: While my great'grandfather's baptistimal record is clear (it states his birth date, baptism date, parents' names and sponsors' names)...what is not so clear is the *name of his exact parish.*

The record just says "Parish: Wexford; Diocese: Ferns."

Does that mean my great-grandfather's exact parish is actually "Wexford Town?"

If not, how can I tell from looking at the record? (and if the record isn't the place to get that answer, where do I look to get that detail?)