from Wikipedia:
Race or racial group usually refers to the categorization of humans into populations or groups on the basis of various sets of heritable characteristics. The most widely used human racial categories are based on salient traits (especially skin color, cranial or facial features and hair texture), and self-identification. (i.e. mostly based on outer appearance)
Ethnicity or ethnic identity is marked by the recognition from others of a group's distinctiveness and the recognition of common cultural, linguistic, religious, behavioral or biological traits, real or presumed, as indicators of contrast to other groups. (i.e. mostly based on cultural, linguistic, behavioral, or religious traits)