Angel
Angels are spiritual beings believed to serve various deities. Although their name comes from the Latin for "Messenger", their association with the Abrahamic religions in the real world means that the standard perception of angels is as magical spirit-beings allied to Good, who stand in opposition to fiends such as demons and devils. Actual use of the term "Angel" can be seen as rather taboo due to various unpleasant attitudes and views towards real-life religions, so sometimes Celestial is preferred as a less-loaded moniker.
In Dungeons & Dragons
In Dungeons & Dragons, "Angel" could traditionally be seen as a generic term for an Outsider from the Upper Planes, although traditionally the term Celestial is preferred for that, due to the Satanic Panic of the 80's.
There are four distinct species of Celestial in D&D; the Lawful Good Archons, the Neutral Good Guardinals, the Chaotic Good Eladrin, and the Any Good Aasimon, who are literally the "conventionally angelic Celestials".
In 4th edition, Celestials as a whole disappeared and were replaced with Angels. Harkening all the way back to their original Biblical portrayl, the Angels of 4th edition are an Unaligned race of Immortals; these entities rise from the Astral Sea and exist to serve all gods, good and evil, with equal loyalty and dispassionate competence. Baatezu in this edition became "Fallen Angels", cursed for betraying & murdering their god. Some angels become fascinated with mortal life and choose to forsake most of their immortality to live closer to them, becoming Devas.
In 5th edition, "angel" is the name given to the Aasimon, who no longer try to hide what they're based on.
In Pathfinder
Pathfinder's Angels are literally just AD&D's Aasimon without trying to obfuscate what they're based on.
Monstergirls
 | This article or section is about Monstergirls (or a monster that is frequently depicted as a Monstergirl), something that /tg/ widely considers to be the purest form of awesome. Expect PROMOTIONS! and /d/elight in equal measure, often with drawfaggotry or writefaggotry to match. |
Angelic monstergirls sit in a weird nebulous position between being entry-level to the fetish and being deep into the fetish. Whilst they rarely if ever look "monstrous" - most appear as just beautiful human women with odd markings, weird coloration for the skin/hair/eyes, wings, or any combination thereof - their religious connotations makes the idea of sexualizing them rather uncomfortable for some individuals. For others, that tinge of blasphemy just makes it more appealing - besides, aasimar have to come from somewhere, and saying it's all due to sinful mortal women tempting angelic men is the kind of shit that started going out of fashion in the 70s.
Angelic monstergirls are usually demure, sweet, understanding, and place far more emphasis on romance over sex. Japanese takes, however, can be much more slutty, in no small part because the fact they were never Christianized means they have no particular reverence for angels. A perfect example of this is Naniel, the angel from Queen's Blade who wants to use her time in the mortal realm to build the biggest reverse harem of sexy men that she can.
In the Monster Girl Encyclopedia, angels are blonde-haired, blue-eyed lolis with halos and golden-white-feathered wings emerging from their hips (an idea stolen from Darkstalkers). Serving as messengers of the gods, angels are becoming increasingly tainted by the demonic energies permeating their world, causing the once-virginal mamono to become increasingly open to sex as a way to spread joy and love to the mortals they wish to protect.