There are two major types of magnetic levitation for trains.
Electromagnetic levitation: German Transrapid, Shanghai Maglev.
Electrodynamic suspension: two subtypes.
With superconductors, relying on diamagnetism: JR Maglev
Without superconductors, relying on ferromagnetism: Inductrack, Hyperloop.
It is very surprising that the superconductor subtype was developed (to a working full-scale prototype) before the non-superconductor version. Superconducting magnets seem much more expensive and difficult.