Some people think manchester is in lancashire? Okay - maybe if you live in, say, bury . but manchester is definitely part of greater manchester!
Before Gtr Manchester was created, Manchester was pretty much split into Lancashire and Cheshire. So its pretty understandable why people may still say it is part of Lancashire.
Postally its lancashire in the north, cheshire in the south. administratively its greater manchester. if you go in even further detail, parts of the area that are postally manchester, are administratively parts of the boroughs surrounding-oldham, rochdale etc.
my address is middleton, which is part of rochdale, then manchester, lancashire. even though we're under oldham council and actually live in chadderton
There is a Birmingham on the Moon apparently. Someone said about Manchester being in New Hampshire, which is in the USA, so I used another English place name outside of England