@contrex,
In Canada, or at least my neck of the woods. We would refer to people from China, Vietnam, Philippines, Japan as Asian.
I say black or African, if that's their descent, not African-American. Or more specifically, if their Jamaican or Sudanese. Anyone from the Subcontinent would probably be referred to as brown or East Indian, rightly or wrongly.. at first glance. We've pretty much stopped called our First Nation's people Indians.
However, our cities are pretty diverse and most of us have friends and family from wide circles. You get used to seeing all manner of faces. Slavic cheekbones, pale blue eyes, freckles, afros, braids, all shades of colours too. South Americans, Central Americans.
I gets too complicated, so we tend to pick a background and stick with it. On the news, I would be refereed to as Caucasian or white, but I'm Irish. My friends are Chilean, Italian, Lebanese, Ukrainian... family members are Native, French, Thai, Chinese, Jamaican...
It's very Canadian thing.. I dunno. Our labels are a bit contrived or complex, but it's far better than the slurs.