Difference between Kumiho(Gumiho) and Kurama

Question

Kumiho and Kurama are two different names identifying the one and only nine tailed fox...

Is there any specific difference like Powers and abilities that relates to the mythology

Some even call it Gumiho

Now I'm confused

Answer 1

The Naruto wiki points the Mount kurama as a possible source of the name Kurama in Naruto series

"Kurama" (九喇嘛) literally means 'nine lama'. Kishimoto was mainly inspired to create Kurama based on the character with the same name from the manga series Yū Yū Hakusho. The name may also reference Mount Kurama (鞍馬山), the sacred mountain said to be the home of the Tengu Sōjōbō who taught people ninjutsu and other Japanese martial arts.

and the name has nothing to do with the nine tail fox or fox spirit other than in the series

Whereas Kumiho(Ghumiho) is said to be the fox spirit in Korean legend

Wikipedia:

A kumiho (gumiho) (Korean pronunciation: [kumiho]; Hangul: 구미호; Hanja: 九尾狐, literally "nine-tailed fox") is a creature that appears in the oral tales and legends of Korea. Deriving from ancient Chinese myths and folklores, a fox that lives a thousand years turns into a kumiho, like its Japanese and Chinese counterparts.It can freely transform, among other things, into a beautiful woman often set out to seduce boys, and eat their liver or heart (depending on the legend). There are numerous tales in which the kumiho appears, several of which can be found in the encyclopedic Compendium of Korean Oral Literature (한국 구비문학 대계).

So if we talk mythology ....there is no connection between Kurama and Kumiho(ghumiho). As kurama is a fictional name for nine-tails in naruto series and has nothing to do with the mythology