There isn't really a difference, it's the difference in the population and courses held.
a metropolitan area is surrounded by suburbs and a city is just one city
Metropolitan University of Tirana was created in 2011.
Metropolitan University College was created in 2008.
Cardiff Metropolitan University was created in 1996.
Metropolitan State University was created in 1971.
London Metropolitan University was created in 1896.
Swansea Metropolitan University was created in 1992.
Leeds Metropolitan University was created in 1992.
Manchester Metropolitan University was created in 1970.
Tokyo Metropolitan University was created in 2005.
Dublin Metropolitan University was created in 1998.
Metropolitan University of Educational Sciences was created in 1981.