Wuxia: Martial arts, but nothing else, People practice martial arts. They are mortals and their goal is not to be immortal.
Xianxia: Wuxia + C-nese magic-based mainly on Daoism
Xuanhuan: eastern fantasy, Might have cultivation, but it's more fantasy than anything

My recommended Wuxia story [Which is QT but all the worlds are related to this genre]

[No CP] [Comprehensive Martial Arts] My life will stop  【无CP】[综武侠]吾命将休

[Comprehensive] Zhao Ru Sun and Moon_Little Fox Xili [End + Fan Wai]     [综]昭如日月_小狐昔里【完结+番外】

A favorite Korean manhua  -> Trinity Wonder

Jianghu/kangho: the most generalised answer is “The part of the world the imperial court doesn’t have direct jurisdiction over.” You are talking about brothels, gangs, bandits, slums, the underworld, rogue disciples from various sects and more. There's no order and rife with crime. It's like taobao, lol. Wulin/murim: refers to specifically and only to martial arts schools/sects/cults etc. The wulin is considered the refined, respected and virtuous people in society; they're also placed higher on the hierarchy. There's order. If jianghu is taobao, Wulin is Tmall.

# For those who don't know what's going on ^^

https://www.wuxiaworld.com/page/general-glossary-of-terms

https://owlcation.com/humanities/A-Beginners-Guide-to-Wuxia

https://owlcation.com/humanities/A-Wuxia-Glossary