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Why does an electrical shock feel painful?
You might also ask, why does anything feel painful,
or why does anything feel anything at all?
All sensations travel along the nerves in electrical
form. There is some chemistry at the beginning and
at the end, but the vast bulk of the distance is
covered by the electrical pulse. It's basically a
wave on a transmission line. It's a rather badly
overdamped transmission line.
Part of the stock-in-trade of being a mammal is
having /myelin/ to reduce the capacitance of the
neural transmission line, thereby increasing the
speed and the fidelity of transmission.
If something happens to your myelin, it's a Bad
Thing, e.g. multiple sclerosis, Guillain-Barré,
et cetera.
An electric shock couples to all the neurons,
willy-nilly, including not just the pain neurons
but also other sensory neurons ... and also
motor neurons running the other way.
=========
As for tissue destruction, sure, if there is a
large amount of juice it will destroy tissue, with
many consequences including long-lasting pain ...
but the threshold for exciting a neuron is many orders
of magnitude below the threshold for damaging tissue.
In fact, transcutaneous nerve stimulation is widely
used for therapeutic purposes.
http://www.webmd.com/pain-management/tc/transcutaneous-electrical-nerve-stimulation-tens-topic-overview
If you want to couple to neurons, DC not optimal.
You want something that looks more like a typical
neural pulse. This is why low-frequency AC (e.g.
50 or 60 Hz) is vastly more dangerous than either
DC or high-frequency AC at comparable voltages.
There's a tremendous amount of interesting physics
in neurophysiology. There are fat books on the
subject.
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