Let's see if I help or make this worse. This gets complicated with people having dens/family rooms/living rooms.
I am discussing the use of these terms in the home. The sala is the main room in the home where the occupants of the house spend most of their time 'hanging out. This is the living room, although some people have family rooms or dens that serve this purpose.
The salón is a large room where guests are received. You can sit and have tea/ drinks, chat, play parlor games or whatever. So this is more like a sitting room or parlor, although people with family rooms/dens will often refer to this as the living room. For some people, these will be the same room. It depends on the age, size, and style of the home.
As for those curious about the English word salons, this is the same word. Salon/salón in general is a space for guests to be entertained. This eventually evolved in some places into a place where a host would gather 'fashionable people' to refine their tastes whether it be art, fashion, philosophy, etc. This is why the most common English usage of the word refers to the studio of a hairdresser/cosmetologist. The stylist hosts you and refines your style. This isn't the only meaning of the word; it's just the most common. Salon in English is still a reception area for company. It's just less common in this general meaning.
It's an entryway where you remove boots, hang cloaks, & park umbrellas. I think a "vestibule" is slightly larger, and folks actually congregate there to meet & greet before entering the inner living area. In case you were wondering. But don't quote me on either, it's just what I recall from my youth...
So for the translation "hall" - what kind of hall are they referring to? Since the other translations are living room and sitting room, I'm guessing it means the more archaic definition of hall as the main room in the house or a large function room, as opposed to a hallway/corridor.
timstellmach, I agree; we do usually shorten the word hallway (passageway), so "hall" does have two very different meanings. We use other words WITH "Hall" to describe PUBLIC Convention Halls, etc., as another person mentioned.
I would bet in 95% of average U.S. homes built since 1900, halls are short, windowless passageways leading to bedrooms, bathrooms, or utilitarian areas like laundry rooms or basements -- not at all like a salon! I would also bet very few people in the U.S. have a room they call a "salon" in their homes. (Quizas the very wealthy!)
We normally give "salon" a connotation for far smaller public gathering places, where groups discuss things among themselves (or get their hair & fingernails done), rather than a "hall" where speakers talk & audiences listen.