J. Clarke wrote:

The distinction is generally that the "resin" in varnish is soluble in
the carrier--recoat and it blends right in.

Not IMO unless you consider shellac and lacqer to be varnish. Which I
don't.

Cured polyurethane is not
soluble in much and certainly not in the carrier solvent.

Neither is alkyd or phenolic resin, acrylic either for that matter.