Nihilism is the wrong thinking that there is no karma, no cause
and effect, no rebirth, etc.
Non-attachment just means you no longer grasp or attach to wrong
notions of self and the world... and attached to possessions,
etc.
An example of nihilism: there is only one life, so why bother about
doing good?
An example of non-attachment: the body is not me and mine,
therefore seeing the body as impermanent and not-self, grasping to
it has ceased.