Fae

Fae (フェイ Fei), otherwise commonly referred to as Neighbors (隣人 Rinjin), is a race of magical beings that have the ability to conjure Magic for either themselves or to aid others. While they can be found all over the world, they are ruled by Titania and Oberon who presides within the Faerie Kingdom, Tir na nÓg.

Ariel
Small and bird-like creatures. They look innocent but are quite mischievous. They assist with the power of wind, an element best for purification and guiding.

Banshee
A fae that cries alongside the pain of her clan and heralds the death of a clansman. Their screams are akin to the sound of wind gusting through the cracks at night. They feel at a loss when their clan dies out, and there is no longer anyone that carries the same burdens and sorrows.

Church Grim
Also known as a Black Grim, a Church Grim is a pure black dog that resides near a church and chases away grave robbers. It is possible that a normal dog can be become a Church Grim. Usually, they are only dogs, but Ulysse, who thought he was human, can transform into a human. In most regional folklore, the "black dog" is an omen of death and malice.

Brownie
Helpful faeries that like to live in houses and gardens. They include Silkies, like Silver Lady. Milk or cream can be set above the fireplace as a gift for a hard-working brownie. While this is said in the series, in Irish lore Brownies described as being mischievous faeries that will only become servants of the person that manages to catch them. How Brownies are described in-series is closer to the classical description of a Hobgoblin. Also, people often confuse the pronunciation of this of faerie as being the same of a popular sweet, the proper pronunciation of this faeries' name is Broo-Nee, it sounds like you are saying the compound of the words Brew and Knee right next to each other in that order.

Changeling
Faerie that is placed in the crib of a human child who is taken by fairies. Changelings that live are raised by humans but notice they are different as they age much slower in adulthood. Shannon is a changeling, who married the child she replaced when she returned to the Anthill.

Elf
Humanoid, with long pointed ears. Flowers bloom where they dance.

Fire Sprite
Fae that looks similar to Ariels, but cloaked in flames, and with paws for feet.

Muryan
Muryans are a type of fae capable of transforming into ants that appeared during the time Silky was alone while Elias and Chise were in Tir Na Nog. The word ' muryan ' itself means 'ant ' in Cornish language.

Selkie
Selkies are said to live as seals in the sea but shed their skin to become human on land. Lindel's familiar, Merituuli is a selkie.

Vampire
Bloodsucking faeries. There are subtypes like Redcurrant, a Leánnan sídhe that exchange blood for talent.

Vodyanoi
A type of water spirit. They have webbed feet, scales, and a tail. The element of water is good at holding, storing and preserving things. Angelica's familiar, Hugo, is a Vodyanoi.

Trivia

 * A fae is a type of fairy in European folklore, a form of spirit, mythical being, or a legendary creature.