Creatures form a set of diverse character types in American Horror Story. Most of those depicted are humans that have been modified (either while living, or crafted from cadaver parts) through magic, science, or an unknown alchemical process with elements of each.
In "Murder House"
Infantata is a crafted entity, created by Dr. Charles Montgomery from the remains of his murdered son Thaddeus. In addition to his own son, Charles crafted other chimera as well via a form of crypto-taxidermy, but there is no evidence that any of these attained any consciousness.
Bastien, a house slave of Delphine LaLaurie, was tortured and mutilated by her. This culminated in her execution of him by placing a severed bull's head over his own, as she rejoiced in having made her own Minotaur.  He was reanimated by his lover, Marie Laveau.  Over time, the bull's head has integrated itself to his body and he developed additional bull-like characteristics. 
These corpses have been reanimated by magic. They are merely puppets of the ritual caster, such as those raised by Marie Laveau to exact vengeance on her enemies. The end result seems largely based on the intent of the caster and the rite used.
Please note that this is different from those who have been restored to life by the resurgence ability. Those affected are no longer dead and are alive, not undead.
Immortals are humans that have been fortified to be unaging, and eternally require no sustenance. They are not immune to injury, but their individual body parts will continue to survive once severed.  Marie Laveau gained immortality by making a pact with Papa Legba, which entailed her having to sacrifice an innocent soul every year at an allotted time.  Delphine LaLaurie was cursed with immortality when she drank a vial of Marie Laveau's tears - a punishment enacted by the Voodoo Queen for her torture of black slaves. 
The Afflicted, also known as Vampires, are humans who have been infected with an ancient blood virus.
They seem to look exactly like regular humans, oftentimes known for being "beautiful" due to one attractive afflicted spreading the virus to another attractive person, though they can also appear average. Upon being turned, a human inflicted with the virus dies before returning to life as one of the afflicted, stripped of their mortality; a person who is already dead can also be brought back to life via the virus's effects. As a result, the afflicted have very pale skin and low body temperature, at 75.5 degrees.
They cannot age or grow old since they stop aging once turned; Ramona Royale compares this to being "frozen in amber". The virus causes biological changes in the hosts, endowing them with heightened senses and greatly increased physical abilities such as a supercharged immune system, granting them immunity from illnesses, diseases, viruses and other infections. They also possess a variety of superhuman physical abilities, including enhanced strength, speed, agility, reflexes, senses, endurance, durability and accelerated healing, as well as the power hold sway over their chosen victims' minds, enthralling them in order to feed on their blood.
They have increased sensitivity to light, especially sunlight, which momentarily weakens their supernatural qualities. They cannot appear in photographs, as still images of them appear blurry and unidentifiable, mistaken for technological problem by the unwary. They don't die from starvation and suffocation, but can be killed via severe physical trauma or firearms, due to hemorrhages and bleeding. Their blood virus cannot heal mental illness, such as dementia or Alzheimer's, and merely halts these illnesses from progressing opposed to healing the neurons.
NOTE: The term "afflicted" is used as a placeholder here until a term is given inside the show's universe.
ScáthachScáthach is a bloodthirsty immortal witch who practices ancient dark magic and worships the old gods. She screeches like a vulture, and is able to manipulate human beings into selling their souls to her in eternal servitude. According to Ryan Murphy, Scáthach is the original Supreme, pre-dating the Salem witches by centuries. 
- ↑ Episode: Bitchcraft
- ↑ Episode: The Axeman Cometh
- ↑ Episode: The Replacements
- ↑ Episode: Fearful Pranks Ensue
- ↑ Episode: Burn, Witch. Burn!
- ↑ Episode: Head
- ↑ Episode: The Magical Delights of Stevie Nicks
- ↑ Episode: Boy Parts
- ↑ Ryan Murphy Confirms Lady Gaga’s Character Is The Original ‘American Horror Story’ Supreme.