Just for the record, in the context of 2 component automotive finishes, the two terms urethane and polyurethane are synonomous and can be used interchangeably.
For those interested in learning more: A urethane linkage (-NHCO0-) is the reaction product between a hydroxyl group (-OH) and an isocyanate group (-NCO). The prefix poly- simply means that the product is a polymer containing the said linkages.
In most automotive topcoats nowadays, the hydroxyl component is an acrylic resin with pendant hydroxyl groups, and the isocyanate is a biuret or trimer of hexamethylene diisocyanate. However, other types of urethane finishes also exist in primarily non-automotive applications, such as polyester-urethanes, vinyl-urethanes, or alkyd-urethanes. One also can encounter the so-called oil-modified urethane varnishes in architectural applications, which are single component products which cure by oxidation (with the urethane linkage being present in the backbone of the polymer). Finally, there are moisture-cured products, which are multifunctional isocyanates that react with atmospheric moisture to crosslink and cure (eg POR-15).
I hope people don't find this boring or rambling.