These are some ideas of classifications:
* Celestials: it refers to any creature (good or evil) which comes from another place, usually from the skies (literally [planets] or metaphorically [heavens] speaking).
* Angelical: from angels.
* Heavenly: creatures (not necessarily angels) from the heavens.
* Devilish: from the devil.
* Hellish: creatures from the hell, not necessarily demons. They may be souls or another stuff from there.
* Infernal: any creature which inhabits the hell.
* Sacred: creatures considered sacred by some religion.
* Holy: sacred creatures with "holy" power.
* Unholy: profane or unholy creatures.
* Undead: creatures that were dead, but now they got reanimated.
* Divine: creatures with divine power. Divine doesn't mean sacred or good, it only means "godlike" power.
* Upper: creatures from upper planes (like heaven or another place in your fantasy world).
* Lower: creatures from lower planes (like hell or another place in your fantasy world).
* Median: creatures from median planes (like our world or another place in your fantasy world).
* Extraplanars: creatures from other planes of existence.
* Extradimensionals: creatures from other dimensions.
* Extraplanetary: creatures from other planets.
* Humanoids: creatures with human-like shape and appearance.
* Commoners: humans.
* Fantastic: fantasy creatures.
* Fairy: fairy-like creatures, with mystic nature.
* Mythical: fantasy creatures but even rarer in fantasy worlds, usually mystic and powerful or difficult to find.
* Legendary: more "mythic" than mythical creatures itself, only found in legends or tales.
* (Un)Sentient / (Un)Speakable: creatures (not) able to think and usually talk.
* Salvage / Wild: animal creatures, wild.
* Primordial: creatures of primordial existence, formed before everything, even time or space itself, outside the realm of physic or before the existence of physic (usually primordial gods make physic).
* Elemental: creatures of elemental existence (fire, water, earth, air, etc).
* Aquatic: creatures that live underwater or are water elementals / from water planes.
* Underground: creatures that live underground or are earth elementals / from earth planes.
* Aerial: creatures that live on air itself or are air elementals / from air planes.
* Incendiary: fire elementals / from fire planes.
* Timeless: creatures that aren't affected for time itself, are immortal or related to time itself.
* (Im)mortals: creatures than can (not) be killed.
* Day: creatures of light, day and good.
* Night: creatures of darkness, night and evil.
* Twilight: evil creatures of darkness or creatures that don't belong either day or night. 227