While race is a human construct based on minor physical differences amongst people, for example, skin color or hair texture, ethnicity is a means of sorting people based upon culture and geography, a construct that is social and sometimes hereditary, that is, based upon the culture and geography of one's ancestors. By culture, I mean attributes such as religion, language, tradition, and art. These categories may or may not overlap, depending on the circumstances. In today's world, where people are more free to choose their own cultures and where people intermarry more freely and commonly, I would argue that both means of categorization are of increasingly limited utility, used mostly to collect statistics to tell us how diverse a particular place is or to make us more culturally aware and sensitive. These are not bad reasons to categorize, but as fewer people restrict themselves socially or maritally, it is going to become difficult to say what one's ethnicity actually is, particularly when most information collected is based upon self-identified ethnicity, or race, for that matter. The other major way that ethnicity is used is as a means of promoting nationalism and patriotism, sometimes for good, but sometimes with disturbing consequences. Some examples will serve to show how complex all of this really is.
Let us take two people who are of Indian ethnicity, that is whose immediate ancestors who are from India, both of whom live in the United States. One of these people may participate fully in the Hindu religion, speak fluent Hindi, dress in a traditional Indian way, and maintain Indian traditions. Such a person is likely to consider him or herself to be ethnically Indian, even if that person is an American citizen. The other person, who is also an American citizen, may have completely abandoned all Indian traditions, attire, and religion. When the census taker comes knocking, this person could say he or she is ethnically American. If the census taker balks, the person could very well point out that the ancestry is Indian, but the person identifies ethnically as an American. That is the person's cultural and geographical basis, so there is a perfectly legitimate argument for this self-identification. And that is what the census taker must write down.
Now let's look at the offspring of a marriage of a Russian-Jewish person and a Catholic from Brazil. Both cultures, languages, and religions are acknowledged and preserved by the parents. What is the ethnicity of the children when they achieve maturity? They may identify as Russian or Brazilian, Jewish or Catholic. Depending upon the skin color of the Brazilian, black or white race might be part of their identification. They, too, may very well tell a census taker they are simply American. None of these would be incorrect answers, certainly, and anything else would take far too long!
For the purposes of promoting nationalism and patriotism, ethnicity is more of a political construct and attitude. The genocide in Rwanda, not so many years ago, was the result of ethnic "cleansing," an attempt to rid the country of one ethnic group. In Hungary, as we speak, Hungarians are reluctant to allow refugees in. This is to some degree because of the ethnicity of the refugees. Hungary is unusually ethnically homogeneous, with few people of ancestry or culture other than Hungarian. This creates a kind of fear about the preservation of the culture and ethnicity and concern about the difficulty of assimilation. This is not necessarily a good reason for the Hungarian stance, but it is, nevertheless, part of the mentality. On the other hand, Germany is welcoming thousands of ethnically diverse refugees. It has a heterogeneous culture, with people of many ethnicities, and it also feels it has something to prove, due to its own history of ethnic cleansing under the Hitler regime.
It is wonderful to celebrate one's heritage and to identify with a social and/or geographic group. It is a good idea to have an awareness of varying ethnicities, since such awareness promotes better understanding and is more likely to lead to harmonious relationships. But these means of categorizing people have been rendered quite difficult with the advent of the free mixing of cultures, and certainly, using ethnicity as a basis to rid a nation of others or to use it as a basis to reject people who are fleeing for their lives makes this means of classification a dangerous weapon.