From classical Greek, 'polis' means 'city' and 'meter' means 'mother', so strictly-speaking a metropolis is a mother-city...eg Canterbury can be considered a metropolis, being the chief cathedral city of England.
In moderrn usage, however, the word is frequently used just to mean anyhuge city including its suburbs. In other words, there really isn't much difference.
I think in practice metropolis and metropoolitan are used of really big cities, as QM says. London's a metropolis. Plymouth's just a city. I'm not sure where the cut-off comes, though.