Turkish bath
Refers to a traditional Turkish-style steam bath. In Japanese, this term is now largely historical and has been replaced by ハマム (hamam) for the actual bath, due to the association with sense 2.
There used to be public baths called 'Turkish baths' in Japan, but they are rarely seen now.
soapland; brothel with bathing
Dated euphemism for a soapland (ソープランド), a type of brothel where customers bathe with prostitutes. The term fell out of use after protests from the Turkish government in the 1980s, and ソープランド became the standard term.
See also: ソープランド
In the Showa era, 'Turkish baths' were known as a type of adult entertainment business.