Manchester has a Lord Mayor, which is a ceremonial role filled by a councillor from the city council.
Andy Burnham is the Mayor of Greater Manchester, which encompasses not just Manchester but also 9 other regional boroughs (Salford, Bury, Bolton, Wigan etc).
London has 30 Lord Mayors, and one metro mayor.
Joe Anderson's role in Liverpool is effectively leader of the City Council, and then there's a Lord Mayor (Anna Rothery), and then a Metro Mayor (Steve Rotherham).