Then the word you're looking for is likely Han, Chinese is only a nationality, not an ethnicity.
From wikipedia, which links to what seems like a relatively reliable source:
> The Singapore Department of Statistics broadly defines "Chinese" as a "race" or "ethnic group", in conjunction with "Malay, Indian and Others" under the CMIO model.[10] They consist of "persons of Chinese origin" such as the Hokkiens, Teochews, Hainanese, Cantonese, Hakka, Henghuas, Hokchias/Foochows, Shanghainese and Northern Chinese, etc."[11]
So I would, on the balance of things, think that kccqzy meant what they said, and was pretty correct about it.