INZ 1017 form has also section for partner, only child section needs to be filled or partner info section is also required to be filled in 1017 form.
You put the child's details as the principal applicant - it is the child who needs this visa. But obviously, one of the parents signs on the child's behalf. And you leave the sections for partner and child blank.
Work visa or visitor visa both have same evaluation process or different (i mean work visa required more check and extra documents or same requirement as visitor visa for spouse)
As these are both the partner sponsored kind, I don't think there is any difference. They will be checking your partnership, and I expect you have seen the many old threads on here where people talked about the proof necessary for that.