Around these parts, "Asian" is shorthand for "East Asian", ie Chinese, etc. "South Asian" is sometimes used for the Indian subcontinent, although oddly enough around here people from India often refer to themselves as "EI", meaning "East Indian". I guess it's all contextual.

For sure, Richmond is the most East Asian city in North America.

I understand what you mean, but when Vancouver locals say "asian", they really mean "east asian" (Chinese/Japanese/Korea). I live in Surrey, a Vancouver suburb, where ethnic Indian is about 30%-40% of population. The local newspaper often refers them as "South Asian community".

But I'm surprised that BBC use "Asian" to refer "East Asian". I'm under the impression that in UK, they use "Asian" to refer "South Asian".

UK person here. Many (most?) people would say you were "Asian" of you were from anywhere in Asia apart from the Indian subcontinent.