Why is fingernail paint called "nail polish"?
It's a holdover term from the early days when nails were indeed polished, instead of painted (or laquered) as they are today.
Here's a good chronology.
Possibly due to their origin. According to the Chemical & Engineering News, August 11, 2008, p.43 (which is taken by me from Wikipedia), the portraits shown of Incas decorating their nails with pictures of eagles include shiny nails. "Nail polish" could have been termed due to this shiny appearance.