Neko (term)

Neko (猫, ねこ) is the Japanese word for a domestic cat.

Mythology
In Japanese mythology and folklore, Bakeneko (化け猫) are cat yōkai, spirits with supernatural abilities akin to those of the kitsune or tanuki &mdash; specifically a type of obake, yokai who are shapeshifters or have shapeshifted. A cat may become a bakeneko in a number of ways: it may reach a certain age, be kept for a certain number of years, grow to a certain size, or be allowed to keep a long tail.

Nekomata (猫又) are another type of cat yōkai, whose tails split in two. They are sometimes considered a kind of bakeneko, and sometimes separate from it; as the word obake has became synonymous with yōkai in common usage.

Nekomimi
Nekomimi (猫耳, literally cat ear[s]), also known as Nekomusume (猫娘 "cat daughter"), or more commonly as catgirls, are human female characters with cat traits, such as cat ears, tails or other feline characteristics; they are a kind of kemonomimi (human characters with animal traits). Nekomimi are prevalent in the anime fandom, either in anime and/or manga media, or portrayed in cosplay.

Neko and furry
As characters, cats (and nekomimi) are not considered furry per se, all though they can be also found in furry art, fursuiting, and as a basis for role play characters or fursonas.