Sauna is of wood paneling/construction and provides dry , a dry heat
Steam room is glass/fibreglass steam is like fog like a thick fog in the room. humid heat
as for a sanarium , never heard of it
but a quick google shows that a sanarium is a type of sauna. In fact it lies somewhere between a sauna and a steam room, combining the benefits of both in a more moderate form.
the benefits of them is that they promote lots of sweating cleansing the toxins out of your body
which one is best i wouldn't know