Are British and American people the same?

Of course you can say that. The main race can be roughly said that the main race in Britain was formed during the Germanic invasion of Europe, mainly including three Germanic races: Angles, Saxons and Jutes. The United States was a British colony after Columbus discovered the New World in 1492, and the time of the declaration of independence was 1776, with an interval of less than 300 years, so it was generally British. However, the local natives are Indian aborigines, and we all know that American society is a melting pot. This view also applies to the perspective of ethnology. Nowadays, the proportion of non-British descent among Americans is increasing.

Back to your question, we can still say that Britain and America are the same race.