(Pure) angel: (plural is angels) Plain and simple, angels are what humans lacking sins become when they die, or sinners who have prayed for forgiveness in their lifetime, they have all their previous memories from when they were a human. When born into Heaven
Horned angel: (plural is Horned angels) Almost the same as regular angels, but these ones are souls who died and went to Hell as a Recontas or Hybrid, only to later become angels for whatever reasons that deemed them worthy. Reasons being things such as; their one sin as a human had since been repealed and they were allowed a free pass into Heaven because of it. Or they had lived in Hell long enough without sinning, and asked for God's forgiveness, on extremely rare occasions, they are to become angels. And just like standard angels, they are not granted wings at first, in fact, before they finally can achieve them, they have large horns on their head to signify to all that they once were demons. They are greatly looked down upon and are only truly accepted in Heaven's society if they gain wings which replace their horns, but their reputation still remains. Even God finds them to be scary to look at, knowing a soul is out there and saw the horrors of Hell and become one with it all, they're unpredictable to Him, but He forced Himself to give them all a chance for true peace. Even if one chooses to replace their horns with wings, Horned angels are still legally known as being Horned; even if one chooses to only refer to themself as an angel with no special title.