In London they're called 'Underground trains', even when they run on the surface. If you need to distinguish, specify 'surface': The District Line is a surface line mostly, but it goes underground near the centre. The smaller ones, which go through circular tunnels, are also called 'Tube Trains' - and people aren't very careful about the size/type of train; you 'take/catch the Tube', even if it's not strictly a tube train
In other cities they're called Metro systems - following the European model. (I don't know which came first, the Paris Metro, or London's Metropolitan Line, which was the first section of the London Underground.