Is there any difference between a molecule having $\vec\mu=0$ and being Non-Polar?
$\vec\mu$ is just the electric dipole moment. However, a molecule can be polar with $\vec\mu=0$, as polarity has to do with charge separation, so a particle with any form of multipole moment is polar.
Molecules like methane, carbon dioxide, and perchlorate have $\vec\mu=0$, but have some level of charge separation, making them polar (these have quadrupole moments, not sure about higher order moments).
Actually, all molecules are polar by this definition, just that many aren't polar enough for this to matter. Generally, when we call a molecule "polar", we are talking about only $\vec\mu$.