Puella Magi

Puella Magi
Puella Magi is a term used to refer to the Magical Girls of the Puella Magi Madoka Magica series and is itself a rough Latin translation of Magical Girl (with a more correct version being something along the lines of Puella Magica). A Puella Magi is created when a girl forms a contract with an Incubator and receives a Soul Gem. In exchange for her wish, the girl must then spend her life fighting Witches (Wraiths in the new order).

Puella Magi and Witches
It is a Puella Magi's duty to protect the general population from the constant threat of Witches, but later on in the series it is revealed that when a Puella Magi's Soul Gem becomes too tainted, she will turn into a Witch. A Soul Gem can be tainted by many things such as emotions and the use of Puella Magi powers. A Soul Gem must be cleansed by a Grief Seed that is taken from a fallen witch. All this adds up to a vicious cycle of Puella Magi fighting Witches, tainting their Soul Gems, turning into Witches, and being defeated by other Puella Magi who will in turn become Witches themselves. Of course, thanks to Madoka's Wish, this is no longer true under the new order.

Magical Molly! Reboot Series
As Kajiurians did not possess the term "Magical Girl" or "Magical Boy", The term "Magical Girl" is used by Homrue, which is applied to young female humans who possessed the Kajiurian System. However, the term is currently used by human media for a very long time.