Though they may seem like they couldn't be more physically different, angels and demons are two creatures of the same essence, and collectively referred to as Celestials.
The difference comes from the intervening millennia since The Fall, and the energies of The Abyss which suffused those rebel celestials who resided there in those millennia.
The Elohim Edit
Angels, The Heavenly Host
The Elohim were the soldiers of God. Since the rebellion of The Christ Child and the disappearance of God, the Heavenly Host has turned to become the new master of Humanity. The masterless messengers are left to their own devices, and while some are well adjusted enough to want to leave alone and be left alone, most see themselves as Humanity's rightful new masters, and treat the Meek as so much chattel, to fight in their armies, farm and cook and equip those soldiers, and make new chattel for them. They are stern and cruel in their austere demand for purity.
The Elohim take many forms, but are generally pristine, and beautiful, albeit in an alien and terrifying way at times. When they evoke animal forms and traits, angels use bird and mammalian forms almost exclusively.
The languages of the Heavenly Host are Enochian and The Words of Creation.
Demonic Beasts, The Primal Mass
The chaotic beasts are creatures from the primordial chaos. They are something of mercenary forces in the celestial milieu. Their first task on Earth was as part of God's apocalypse, tearing down the works of Man, to prepare a new canvas. Since then, however, much of Chaos has run rampant upon the Earth, doing as they wish, typically destroying all they desire.
The Primal Mass, appropriately, takes on a truly wide, vast and unknowable number of forms, with seemingly no known limits, though bestial reptilian, or nauseatingly rotten human forms seem far more common than others.
The communication of chaos is not a language, and cannot, as such, be learned. All communication with chaos is an assemblage of irregular sounds, and meaning is conveyed through a non-verbal force.
The Fallen Edit
Devils, The Hordes of Hell
The Fallen were those angels who rebelled at the dawn of time for reasons that are unknown to man. The Angels have their story, and some demons have stories that line up, but not all. Some say they fell for their love of man and God's contradictory instructions. Some say they fell because Lucifer could run things better. Some say they fell simply because they got tired of taking orders. But no one is telling humankind, definitively, which it is. Since the rebellion of The Christ Child and the disappearance of God, the hordes have run roughshod over the Earth. Some have gathered to them cults of followers, acting as mentors to dutiful pupils, others serve to keep safe vast stores of knowledge otherwise lost, and some simply while their days in freedom, pursuing their whims.
The Hordes of Hell take just as varied forms as the Heavenly Host, though whereas every Angel is beautiful, even those who are terrifying, every demon is terrifying, albeit sometimes in a beautiful, alluring way. Many devils evoke animal forms or traits, often exclusively reptilian, arthropodic, or oceanic, though the forms of particularly deadly birds and mammals are not uncommon.
The languages of the Hordes of Hell are Enochian and the Dark Speech.