You contradict yourself here. A Friendly AI is an intelligence which attempts to improve the well-being of humanity. A paperclip maximiser is an intelligence which does not, as it cares about something different and unrelated. Any sufficiently advanced AI is either one or the other or somewhere in between.

No; these are two types of AIs out of a larger design space. You ignore, at the very least, the most important and most desirable case: An AI that shares many of humanity's values, and attempts to achieve those values rather than increase the well-being of humanity.