Neko: Nekos are essentially humanoid, but with the ears and tail of a cat. The reason for their existence is simple- horrific human experimentation on the whims of Aozora Chiyumi, who personally finds the concept appealing. Psychologically, they are only a bit different to humans- they have a tendency to purr and can be more dependent than humans. They are not discriminated against, but aren't all too common. Some of them retain a chemical used in their mutation process, which can be transmitted by transferral of some bodily fluids, making many cautious around them in terms of relationships. Currently, there is no method to reverse nekofication.
Tenshi: "Tenshi" means "Angel", but really just refers to humans who have been altered to have magical abilities. Most Tenshi only have minor abilities that they use to the best of their efforts. A select few are chosen to be part of an elite organisation that serves as a powerful magical special operations force. These are referred to as "Densetsu", meaning "legends". There is no way to undo the process of tenshification. Due to the unpredictability of what power a tenshi will have, only certain individuals are forced to undergo the procedure, and are also essentially indoctrinated to be loyal to Kyoki Chudoku in the process.