Yes, or in more detail, DC third rail EMUs USED to use DC motors, and some are still in use. Speed control was achieved by switching the motors in series or parallel and by inserting or cutting out series resistances. Simple and effective but wasteful of power, and a lot of contactors to maintain, and brushes on the motors to replace.
Modern practice is to use AC motors fed with three phase AC from an inverter. The voltage and frequency are varied electronically with but little loss, and few moving parts and no brushes.
Early designs proved unreliable, but recent types are much better.
AC locos and EMUs followed broadly similar practice after transforming the AC to a lower voltage and then rectifying it to DC.