It seems to me that in the US the term 'Asian' refers to Chinese, Taiwanese, perhaps Japanese, Singaporean, overseas Chinese (from the Phillipines or Indonesia, etc.)
East Indians and Pakistanis and I suppose Sri Lankans are more correctly referred to as "South Asians".
'Chinese' seems to be a more precise term. For some reason "Chinaman" is considered some sort of slur, while Englishman, Irishman, Welshman and Frenchman are just fine with the English, Irish, Welsh and French. It's not as though anyone is suggesting that the Chinese man in question is fabricated from, you know "china'.
Is the term 'Chinatown' offensive? I am sure that 'N*gg*rtown is but China is not an offensive word like n*gg*r. Jesse Jackson got in a lot of hot water with the word "Hymietown', although there are surely many men named Chaim, from which the term is derived, in the garment district.
If a person is sort of tall, we can say that they are 'tallish', yet a 'Jewish' person is no less of Hebrew ancestry than a Jew. Jewish does not mean 'sort of a Jew'.
People from the East are from the Orient. People from the West are from the Occident.
Strangely, Oriental is some sort of slur, yet Occidental is never objected to. There is an Occidental University and an Occidental Petroleum. Occidental Life will insure you as well.
In Monopoly, Oriental Avenue was in the low-rent district, though it was more prestigious than Baltic Avenue, which was sort of a gameboard slum.
Rich folks lived on Park Place and Boardwalk. I would have thought that the truly rich could have been able to afford sidewalks made of tile, marble, or at least cement.
It's all rather baffling, isn't it?