I thought neuropathic pain was a pain that essentially was all in your head, but still quite painful.
(pain with no known cause)

Peripheral neuropathy causes pain as well.. like the small fiber neuropathies are quite common with burning pain.
I know a lot of the diabetic neuropathies cause the burning.
From what I have read anyway.

My own neuropathy doesn't cause any pain.. just numbness.

And someone please feel free to correct me if I am wrong.
I'm just going by things that I think I recall.