RV1.20.1 lists the situations where the partner of a principal applicant is eligible for assessment in his/her own right; separation from partner is one of them. This is a generic provision for applications made after the grant of a Resident Visa for one of: a Permanent Resident Visa, a variation of travel conditions on an existing Resident Visa, or a second or subsequent Resident Visa.
Note, however, that the wording is "variation of travel conditions or a new residence class visa". I don't know whether or not INZ will issue a Permanent Resident Visa in this situation; it is conceivable that this is to be interpreted as a second or subsequent Resident Visa under
RV4 (rather than a Permanent Resident Visa under
RV2). However, there is provision for INZ to assess you for a variation of travel conditions or a second or subsequent Resident Visa should they deem you ineligible for a Permanent Resident Visa, provided that you give them permission to do so (
RV2.25). Given this, in your situation, I would tick the box on the INZ 1175 form that allows INZ to assess you against one of these alternatives.
To answer your question about what the difference is between a Permanent Resident Visa, a variation of travel conditions on an existing Resident Visa, and a second or subsequent Resident Visa: the "
Resident to Permanent Resident" information on INZ's website will probably answer this.
EDIT: The wording of RV1.20(b)(ii) seems to imply that you will need to apply in your own right if a provision requiring a secondary applicant to be assessed independently of the principal applicant (RV1.20.1 to RV1.20.20) applies.