Neither of these are practised anywhere in Finland at least. But there are at least one Finnish swimming bath where they had to limit steam competitions and made a button controlled mechanism to administer water instead of free usage. Not because electrical shock prevention but because bad human behaviour per se.

When needing to define type of stove, it's electric stove, wood heated stove. Latter has two types, which continuous wood burning is still common (this stove you can add burning wood during bathing) and older not so much any more used before bathing heated type stove which you cannot add wood while bathing. Oldest type is smoke-sauna, which doesn't have chimney at all. Wood is burnt in stove when heating, then when burnt enough sauna is ventilated first and then bathing starts.

But all these different heating elements are commonly stoves, just adding electric-, wood-, or smoke- stove is added context requiring.

Infra saunas then have those lamps of course, no stove there.