Teaching and Governing are merely aspects of the same Office.
So what? The teaching office is related to the spiritual/doctrinal/Divine/unchanging nature of the papacy, while the Governing is related to the human/fallible/can-be-changed portion of it (i.e. Christ gave Peter the power to "bind and loose").
The OUM is infallible and part of the Teaching office of the papacy. The OM can either be infallible or fallible, depending on how's it's used. The OM is infallible when it reiterates what has "always been taught" as +JPII did when he reiterated the bad on women priests. The OM is fallible when it is not clear that what is being taught is Traditional, Apostolic and "universally believed" as many of the encyclicals of the post-V2 decades have been, since they are filled with a mix of orthodoxy and novelty and thus their ambiguity undermine their authority.
The OUM necessarily is obliged to be believed with certainty of faith, since it is a doctrinal, Apostolic teaching of the highest degree, infallibly protected. The OM has varying, multiple levels of authority attached to it, depending on how the pope teaches, what he references and if he makes use of Apostolic teaching authority, or if he just teaches as a normal Bishop and private theologian. Plus, since the 50s, the definitions and labels for what the magisterium actually is, have changed, been debated and further examined. To date, the Church has not clearly explained the various levels of the magisterium.
Suffice it to say, the Church has an obligation to make it VERY CLEAR that teaching x, y or z is obligatory and to what degree. If they do not, we are allowed to ask for clarification because Scripture says that "there is nothing new under the sun" and apparent novelties have a right to be challenged until the pope teaches with authority. Those heretics who ran V2 used the faithful's trusting nature and docility against them, to imply that V2 was doctrinal, when we now know (from many statements from those in attendance) that it was anything but, and its heretical novelties should be done away with and anathematized...which a future orthodox pope will do someday.