It depends on what one looks at.
The U.S.A., culturally, most famously treats race as if it be an ethnicity. As such, in their perspective what they call “African-American" and “European-American” are very different.
From where I stand, they are all “Anglo-Saxon”, and further subdivisions seem rather minute and trivial. They all live in a similar culture, having grown up with English as a native language, and tend to have very similar Anglo-Saxon cultural sensibilities that are shared with say Australia and the U.K.. that often seem uniquely and recognizably Anglo-Saxon to me.
I do not really think that the color of a man's skin, having grown up in a very similar environment, speaking the same language, practicing the same traditions, and being influenced by the same values, makes him all that different and worthy of a different “ethnicity”.
Many countries actually have a large population of recent immigrants. Did you know that Polish is spoken more in Ireland than Irish as of this moment for instance? These Polish immigrants have grown up speaking a different language, exposed to a different culture, eating different food and practicing different traditions. — they might be as “white” as the Irishman as a stereotype, but there is a greater difference to be had here than between the Anglo-Saxons of different colors.
And, to note, the only Polishman I have ever had a good conversation with was quite dark skinned, but nevertheless Polish was his native language. He lived in the Netherlands but was a recent immigrant from Poland and quite catholic. Apparently both his parents were immigrants as well, but he was born in Poland and spoke Polish as a native language.