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 Murder House. He crafted other chimera as well in 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. Some (like Kyle Spencer) retain or develop sentience. Others are merely puppets of the ritual caster, such as those raised by Marie Laveau to torment her enemies (such as Pauline LaLaurie). 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, and it can be assumed that (if The Minotaur was enhanced by the same method) their individual parts will continue to survive once severed. Delphine LaLaurie and Marie Laveau are two that have been depicted.
As a note, it has not been established whether the effects of the Resurgence magic result in immortality, or are instead limited in duration.
These are humans who have been afflicted by an "ancient blood virus", giving them immortality and durability at the cost of requiring a diet of blood (and possibly sex). Countess Elizabeth is one of the afflicted, and is "extremely strong [...] It's kind of impossible for anything to penetrate her." A number of towheaded youths were shown in promotional teasers prior to the season opener, and may represent other afflicted.
NOTE: The term "afflicted" is used as a placeholder here until a term is given inside the show's universe.