Does that mean that when for example my partner was given a work visa and can't work, it won't affect the next application which is resident?
That is exactly right, if you're talking about a partner-sponsored temporary work visa (which is an open visa allowing the person to take any job offered in NZ). The only requirement for getting this kind of visa is to be living in partnership with a NZ national or resident.
If you happened to have a partner who has a work visa in their own right because they have a skilled job, THAT kind of visa depends on their employment, regardless of who they live with.