There isn't a large difference. Ambiance comes from the French language and atmosphere comes from Latin, but they are both used in English. Of course atmosphere has a larger meaning, you can talk about the Earth's atmosphere or the atmosphere of Mars. But if you're talking about a room in a restaurant you could say "This room has a nice atmosphere" or "a nice ambiance" and they would mean the same thing. I think that ambiance is a more intimate word, it's more personal and cozy.

The word, ambience, has to do with the environment and surroundings that you see. For example, a restaurant could be described as having a casual ambience. The word, atmosphere, has to do with influence and mood you feel. For example, you would use the word, atmosphere, to describe a funeral home or hospital. Both places might have a gloomy and depressing atmosphere. Hope this helps

There's practically none. "Atmosphere" is more common. Use it unless you have a good reason for saying "ambiance." To the best of my recollection, in the United States, the word "ambiance" or "ambience" started to become fashionable in the 1980s. I think it is simply is a fancier word for "atmosphere." Also, "ambiance" is used in a narrower way--it usually means a social atmosphere, at a group gathering, like a restaurant or a party.

Karl is right. I would only add that 'ambiance' is a slightly higher register noun (more formal), at least in British English.