How to know if bad sectors are caused by physical or logical damage?

Solution
Check SMART attributes. You can use HDtune health for that.
Relocated sectors mean - physical damage.
Pending sectors mean -could be physical and could be not.
If basic utilities don't work, doing a *full* format of the hard drive (not the low-level one) can very frequently resolve the issue if you have logical damage.

If no software works, you almost certainly have physical damage, the only thing you can really do is a give the hard drive its last rites before its ceremonial disconnection forever. Requiescat in pace.