SrtaA
Wuxia as the word meaning, it composed of the elements: wǔ literally "martial"/"military" and xiá literally "chivalrous", or "hero". A martial artist who follows the code of xia is often referred to as a xiákè literally "follower of xia. So basically the genre of wuxia is talking about the xiake (follower of xia) who is following the code of chivalry (Xia) usually requires these xiake to right and redress wrongs, fight for righteousness, remove oppressors, and bring retribution for past misdeeds. Often times, wuxia is always set in ancient China - as the wuxia or xiake theme is actually has been around even during the Warring States Era (7 BCE - 221 BCE). But actually there's no restriction for that. I remember there's an Andy Lau's version of wuxia in modern setting.
Wuxia genre is just not easy in modern setting. Because there's law and police. While the xiake tend to be the dark justice heroes. They had to act in Xia code in a time where they could not rely on the law and government to give justice to the people.
Therefore in wuxia genre : the main theme is always fighting for justice. If you're watching Chinese series, The Legend of Condor Heroes, Return of Condor Heroes, The Dragon Sword and Heavenly Sabre, they are all in this WUXIA genre.
While in these past few years, there's another new genre called Xianxia - in which Xian means fairy. This is the genre which involves: long-haired Gods, Heavenly Emperors, long sleeves flowing dresses, scenes under the full moon by a waterfall next to a willow tree (as you mentioned in your post :D ) in Chinese series, this is like : The Lives, Three Worlds, Ten Miles of Peach Blossoms, Three Lives Three Worlds, The Pillow Book, The Untamed, etc.
While, there's also this ANCIENT costume genre -- usually they're just romance talking place in ancient setting. But sometimes even the ancient setting is not clear. Most of the time the author didn't put specific time. It's just in ancient time....don't know when.
Apparently, there are many people who don't know the difference between the genre though. Some people think that as long as there's sword, with the main characters with long hair and robes as wuxia, or historical :D