The two nouns, salon and saloon, come from the same French word; in the past, both words described specific kinds of social venues—places where people gather to talk, play games, listen to music, and perhaps drink alcohol. These meanings are now a little out-of-date, but still in use.
A salon, historically, was a specific room in a home, for entertaining guests. And the word can still be used this way—but only if the room is in a large, expensive, old fashioned kind of home. Otherwise, we do not call such rooms salons anymore. In modern America, we now use the word salon for businesses that provide beauty services, such as hair salons and nail salons. We sometimes now use the word to describe a gathering where people discuss social issues in a relaxed manner.
Saloon, on the other hand, describes a pub (tavern, bar) in the old American west—like the ones in the movies where people gamble and get in gunfights. There are probably no more true saloons—only those for tourists!