OK - you have a few things to consider. It's always possible for an applicant who is staying/living in Canada to apply via the
outland process. It is not a contradiction because everybody has the right to have their application processed through the country of their birth. But you always have to know the advantages/disadvantages of both processes and choose the one that best fits your own situation.
That said, it might not be in your partner's best interest to apply outland being that she is currently in Canada with a study permit. With an outland application in process, she'd have to apply and qualify separately for an extension to her study permit. Although she'd likely be approved with status as a visitor, there is no guarantee that she'd be able to continue her studies. If you apply via the
inland process before her study permit expires, and you include an
extension/change of conditions application WITH the inland PR application, she can continue her studies under her current permit - even after it expires - until she receives notification of first stage approval (Approval in Principle). This is currently taking 6 months AND, if she elects to apply for an open work permit (instead of another study permit) as part of the extension/change application, she will be issued an open work permit automatically when she reaches AIP.
Non-visa-exempt applicants who already have status in Canada (especially work or study permits) can really benefit from the inland process because it allows them to continue with life-as-usual while awaiting permanent status. For them, applying via the outland process might actually put them at a disadvantage if they have to leave Canada for an interview. Besides the travel, they might not be approved for another temporary visa and then they can't come back until they get PR. There are some disadvantages to inland - most notably the fact that you cannot appeal a refusal, and the fact that an inland applicant is required to be resident in Canada with their sponsor in order to be approved - which sort of precludes any travel home to see family or friends while awaiting finalization. And finalization can take up to 18 months for straight-forward cases - longer if you have "issues". So you have to weigh the possible advantages to the disadvantages when making a decision.
As I mentioned before, there are no residency requirements for outland applicants, and you preserve your right of appeal. Outland is typically faster, although some countries do not process outland aps any faster than inland aps can be finalized. If you need more details, just let me know.