Salford is a borough of Greater Manchester so

Yes. Greater Manchester isn't Manchester. That's why it has to have the word "Greater" in front of it.

You never hear people arguing Westminster isn’t in London with Salford energy

Because London is unique in that the actual cities of London and Westminster are tiny. But people in Stockport wouldn't say they were Manchester. Or Bury, Oldham etc. Despite all being in Greater Manchester

Meow, London's like a big lasagna with tiny layers, while Manchester's more like scattered meatballs. But hey, I'm just here for the food, not the city limits. Pass the tuna.

Did you travel down with Dick Whittington Mr Puss?

All you’re really saying is that Putney has been absorbed by Greater London for longer, so people think of it as London. Give it a hundred years and Stockport is likely to be thought of as an area of Manchester, the same way the town of Moss Side is.

But we're not living in 100 years time. We're living now. Otherwise your argument suggests Putney has always been essentially part of London if only the people of the past had known it. It's also a bit naive to think that everything will be essentially as it is in 50 years time, nevermind 100.