Nail polish remover is a compound called acetone, which is extremely volatile. Rubbing alcohol, also called isopranol, is less volatile meaning that it doesn't evaporate as easily. The reason has to do with the degree to which the molecules of each substance are attracted to each other.
Rubbing alcohol has stronger intermolecular forces, which makes it less volatile. The -OH group that's a characteristic of alcohols causes the molecules to be very polar, which means that they have a large separation of positive and negative charge. This is because oxygen attracts the shared pair of electrons in the single bond more than hydrgogen does. As a result hydrogen bonds form in which the slightly negative oxygen on one molecule is attracted to the slighltly positive hydrogen on another. The increased attraction of molecules to each other makes them less likely evaporte at the surface of the liquid. Evaporation requires gaining enough energy to overcome intermolecular forces.
Hydrogen bonding only occurs in molecules that have a hydrogen atom bonded to an oxygen, a fluorine or a nitrogen. Acetone is a polar molecule because its central carbon is double-bonded to an oxygen that has two lone pairs of electrons. However, its hydrogen atoms aren't bonded to the oxygen so it doesn't exhibit hydrogen bonding. With weaker intermolecular forces than rubbing alcohol it's easier for its molecules to escape at the surface.