A steam sauna and steam bath really serve the same function, they are just constructed differently. Steam is generated from an external machine and piped into the room, or steam is created by dropping water onto hot porous rocks which are heated by heaters.
The difference is that a steam saunas humidity is usually low so the the room is contructed with soft woods.
A Steam Bath is typically a room constructed with some type of rock for the walls such as marble, tile, or an acrylic. Many times the steam room is cooler but feels hotter than a sauna.

Steam showers are the same as steam saunas and steam baths in that steam is used to get the health benefits. Steam showers are self contained units that brings the cost of having your own steam therapy down to an affordable price.

There is no difference in the health benefits between the two. They both achieve the same results.

Some of the many health benefits are that the sinuses are cleared and the nasal passages, sore muscles are relaxed, respiratory ailments such as asthma, bronchitis, allergies are eased.

A session that lasts for 30 minutes typically uses less than a gallon of water.

No you should not. Let your body cool down to its normal temperature first.

Yes, infact, most steam showers come with that function built into the unit. Just add your favorite scent.