You're just arguing semantics. When you say "poly" to me, that means
polyethylene, polypropylene, etc. "Poly" by itself really means
nothing, except some unspecified polymer.

Anyway, if there is a polyurethane finish on there now, you should
sand it completely off before switching to "regular" varnish.

Oh yea, and if you want to really learn about "varnish", read up at:
http://en.wikipedia.org/wiki/Varnish
You'll want to decide which of the following types of "varnish" you
need:
2.1 Violin
2.2 Resin
2.3 Shellac
2.4 Alkyd
2.5 Spar Varnish
2.6 Drying Oils
2.7 Polyurethane
2.8 Lacquer
2.9 Acrylic
2.10 Two-Part

You're welcome.