Related in plot/subject certainly, but as a researcher/cataloguer of songs we normally reserve the word 'related' for songs that have some text in common.

As far as I can see 'Willy O' was only printed by Nugent and Birmingham in Dublin c1860 although there are a few sheets with no imprint that look to have come from the same presses, and one of these might be Brereton. I certainly haven't seen anything on broadsides out of Ireland, and remnants of it in oral tradition that can be traced back to Ireland. Someone sang it at my local club on Monday.