Mullany/Mullaney was often interchangable in my family.
GreatGrandParents. Patrick Mullaney m. Catherine Mullaney. Children. Thomas born 7th/9/1895 Burtonwood. Johnborn 28th/8/1897 ditto Jamesborn 28th/10/1899 ditto Denisborn 22/3/1902ditto Joseph born 25/8/1904ditto
Thomas Mullaney (Patrick's bro. or cousin) m. Bridget. Children. Johnborn 2nd/1/1893 Burtonwood. Maryborn 26th/12/1894 ditto Kateborn 26th/4/1897ditto Thomas born 2/9/1900ditto.
The boys became coal miners and moved to areas such as Coventry. According to the 1881 census there were quite a few Mullany/Mullaney's in the Manchester area.
The political boundaries between Lancs & Cheshire have changed a lot over the years.