Race is based on physical appearances, like skin color, and is rooted in asserting power and resources. Ethnicity is a person's social group membership based on a shared language, food, geography, and traditions. Both of these terms are socially constructed and related to each other. This is why it can sometimes be challenging to differentiate between both terms.
Racism are the beliefs, attitudes, institutional arrangements, and acts that put down individuals or groups because of appearance or ethnicity. Racism can show up in overt ways like racial profiling or in more covert ways like microaggressions.