According to Learning for Justice, "Race is socially defined by an arbitrarily organized combination on physical traits, geographic ancestry, language, religion, and a variety of other cultural features. Social definitions of race differ depending on context and always operate in the service of social-dominance hierarchies."
According to Merriam Webster, ethnicity means belonging to a large group of "people classed according to common racial, national, tribal, religious, linguistic, or cultural origin or background."
The distinction we teach students here at Dalton is that, while race is often about external characteristics (skin color, hair type, etc.), ethnicity is more closely tied to a country, or group of countries, and the culture(s) they celebrate. This includes things like food, language, holidays and celebrations, values and more.
Anyone can feel very connected to their ethnicity (or ethnicities), or not connect at all; there is no wrong way to feel about your own ethnicity!