If that side is historically Catholic, it's more likely (not always) to be "Green" Irish. If it's historically Presbyterian (not always), it's more likely to be Scottish.
Many names have been Anglicized both in the US, and in Ireland and Britain. McCarthy/MacCarthy/McCarty/MacCarthy is obvious, but one of my good friends has over 20 variations of his surname in Ireland alone. The four you mention could all come from the same name, or they could be different just due to pronunciations. Picture Paddy, Mick, or Jock arriving in the US or talking to George the Brit with the various Celtic accents. McCoy, McCay, McGoy, McKay, McGaha.