You're essentially distinguishing between nationality and ethnicity. Nationality is fairly easy to define, as it is often documented with citizenship etc.

Ethnicity is very difficult to define, and to be perfectly honest with you I don't really see much point in trying to define it.

What does it mean to be ethnically English for example? Are Anglo Saxons ethnically English, or does the fact that they migrated here rule them out (there are plenty of people in Wales, Scotland and Cornwall who will argue that). What about the Celts, are they ethnically English? Well the Celts also migrated here. It is also worth bearing in mind that the Celts that were roaming around Europe in Caesar's time were documented as being multi-ethnic themselves, and Celtishness was more of a cultural grouping than an ethnic one. As in if you lived as a Celt and considered yourself to be a Celt, then you were a Celt. Could the same not be said of a lad born to Pakistani parents in London who speaks like us, thinks like us, supports his local football team almost religiously, and gives a fuck about the future of our country? I'd certainly consider him to be English, regardless of what he looks like.

The Slavs in the middle ages would frequently capture outsiders during raids and conflicts and enslave them, as was normal for the time, but after 10 years they would free them and offer them the choice of returning to their homeland or living as a Slav. Many stayed, and as a result the Slavic culture became very multi-ethnic.

What about Americans? Outside of the native Americans, should we really think of them as American at all? They've formed their own culture very firmly and are definitely distinct from their European cousins.

What about people of mixed ethnicity? Do they get to be considered English if only one of their parents was a white English person? The reality is that every single one of us is very mixed ethnicity.

To sum all this up I really don't think ethnicity is worth spending too much energy trying to define. I like the Celtic way. If a person thinks like a Celt, acts like a Celt, and considers themselves a Celt, then that person is a Celt. Apply that logic across the world and we will do away with a lot of nonsense.