it is a special member, and in some sense, it is not fully integrated
into EU yet. USA often treats Britain and the rest of EU nations differently,
and vice versa.

Many american scholars as well as British scholars do not want to make Britian
part of EU, because it does not serve their interests well.

China also treats EU and Britain differently.

In formality, yes, Britain is part of EU; In essence, it is clearly no.