What does the term domestic mean in the 1901 Manitoba census?
A girl, age 7, who had been adopted by the family at age 3 is referred to as domestic rather than daughter.
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The term domestic in a census record is very likely to refer to occupations that are associated with working in a household.
For an example, see this passage from Melanie Buddle's book The Business of Women: Marriage, Family, and Entrepreneurship in British Columbia, 1901-51, page 29:
...British Columbia had a large Asian population: at the end of the nineteenth century, up to two-thirds of domestic positions (servants, cooks, housekeepers) in the province were filled by Chinese men.
The instructions for the 1901 Census of Canada say (in section 60):
If married women, other female dependents or children carry on a gainful or wage-earning occupation n any capacity, the kind of occupation will be given, and they will be classed as employers or employees as the case may be ; but if they are only carrying on domestic affairs in a household without wages they are not to be classed as having any occupation.
The census instructions also say (section 42):
In the restricted sense of the term, a family consists of parents and sons and daughters united in a living and housekeeping community ; but in the larger sense it may include other relatives and servants. A household may include all persons in a housekeeping community, whether related by ties of blood or not, but usually with one of their number occupying the position of head.
And in section 48 the instructions say:
In column 6 the head of each family or household will be entered as such, and all others according to their relationship -- as wife, son, daughter, servant, boarder, lodger, partner, etc.
Bear in mind that in most census years we do not know who gave the information about the household to the enumerator. (Two notable exceptions are the 1911 Census in England and Wales, where the original schedules filled out by the heads of household survive, and the 1940 US Federal Census, where the enumerator was instructed to mark the name of the person giving the information with an X.)
Without other supporting information, I would not take any single record as a sign that a child was not viewed as a daughter by other members of the family. Records can have mistakes in them, and no single record is proof of anything.