I'm sorry if I offended anyone - I was simply answering the OP's question with what I've experienced in my particular region.
It seemed to me like the question was '"how do you describe a particular person who looks Asian/Oriental" and which term is correct', as far as the OP put it. I may have misunderstood, but that's what I gathered. As such, going off OP's example of how to describe someone in a train station, I was saying how people are described based on the particularities of their appearance.
Thank you, everyone, for jumping down my throat. Truly appreciate it when I was just trying to answer something honestly. I am fully aware that people who look very different from their supposed ethnicity exist - taking Brazil as an example, citizens can range the gamut of looks. Frankly, they can in every country. The only reason I said 'looks vaguely Middle Eastern' was because I find that it's the region with some of the most variety in terms of looks and it's one of the few regions that doesn't have a particularly strongly defined ethnic image that comes to mind in terms of looks (whereas 'Asian/White/Black/Native America' call to mind fairly distinct images), at least in my mind.
I believe the OP was asking how you would refer to a group based on appearance, and I was trying to clarify.
Editted to add that I don't think it's a great idea to identify someone based solely on apperance (when referring to a vendor, you're better off saying 'that girl/boy by the east exit of the station who sells magazines'), but if for some reason you feel a burning need to do so, that's how I would do it. In my region the ways I've listed are considered non-offensive. Take it as you will.
A secondary note is that the term 'black' is often swapped with 'African-American', though many of my friends have pointed out that they prefer black because they are neither African nor American, or if they are, they simply prefer the term 'black'. That's something that changes from person to person, so it's something you want to listen out for and figure out what the people around you prefer.