They're not Assassins but they are assassins. The Assassin is a class. An assassin has a job. An Assassin doesn't have to be an assassin to be an Assassin, but he makes for a pretty good assassin because they taught him how to be an assassin in Assassin school. Likewise, an assassin doesn't have to be an Assassin to be an assassin, but he may want to look into some things that the Assassin has to be a good assassin (like poisons) and the Assassin school may even be willing to teach him how to be an assassin and even let him take the oath to be an assassin just as an Assassin would. One of the Assassin schools that does this is the Red Mantis Assassins who also employ assassins to serve alongside Assassins.