Glasgow's complexity has to do with the land holdings of Glasgow Cathedral and Paisley Abbey, annexations by later landowners, and the way Glasgow expanded. Glasgow's core is in Lanarkshire and north of the Clyde, bounded by Dumbartonshire and Stirlingshire, and somewhat isolated from the rest of Lanarkshire. Renfrewshire denotes the south of the Clyde, west of the White Cart; Lanarkshire east of the White Cart. Govan however, which is south of the Clyde west of White Cart, belonged to Glasgow Cathedral, but parts of Govan such as Titwood and Gorbals became annexed to Renfrewshire. Equally perplexing some areas west of the River Kelvin, formerly the western extent of Glasgow, were in Renfrewshire, but transferred to Lanarkshire, and eventually absorbed by Glasgow. Part of Govan parish was north of the Clyde (eg Partick). Only in the 20th century did Glasgow start to take in bits of Dumbartonshire to the west or Stirlingshire to north and east. As Glasgow expanded southwards it took in first Rutherglen (Lanarkshire), then Pollokshaws (Renfrewshire), but just to complicate matters parts of parishes remained outside Glasgow in Renfrewshire. Hence Pollokshaws is in the north part of Eastwood Parish, but Eastwood outside Glasgow (Giffnock, Eastwood Toll) is part of East Renfrewshire: likewise the north part of Cathcart is in Glasgow, and the south part (Netherlee, Clarkston)is in East Renfrewshire. I guess this looks pretty confusing. During the 19th century there were quite a few boundary changes and annexations, so residents' county affiliations could change from one census to another.
