Neuropathy is just a more general term. Neuropathy would mean any disease of the nerves. This would encompass peripheral neuropathies plus other problems such as a pinched nerve in the back for example.
Peripheral neurophathy is some disease or process affecting the nerves in a way that the points furtherest from the brain show symptoms first. This usually means first the toes and feet and later the fingers and hands. Symptoms most typically including tingling/burning sensation or a lack of sensation. Diabetes is the most common cause of peripheral neuropathy.
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Yes, in your situation this would be a neuropathy that was isolated to the injured nerve.At least in your situation it will not be a progressive problem.