Actually what I am addressing is who gets to determine the difference. It is my understanding that the Catholic laity is not authorized to make such decisions, and that they are told by the clergy what the applicablelevel of authority and interpretation of any Church teaching, or Papal action or statement, is. So in a functional sense it doesn't really matter what the laity thinks of the difference between Papal opinion and magisterium, because they don't have the authority to implement their decisions on the subjects.
Thank you for that clear explanation; now I understand your point, and it's an important one.
The infallibility manifested (on rare occasions) by a pope is not really the "Pope's infallibility" (as if it were a personal characteristic) but rather the Church's infallibility being exercised in its --- by far --- least common instance.
As the Dogmatic Constitution on the Church (Vat II) expresses it, Sacred Scripture and Sacred Tradition make up a single sacred deposit of the Word of God, which is entrusted to the Church. The papal (or conciliar or episcopal) magisterium depends on this, since anything "divinely revealed" has to be derived from what was handed on to us by the Apostles.
So there's a 2,000 year record out there for all to see, which shows what we are convinced has been derived from this Apostolic (not solely papal) authority. And also out there for all to see, is 2,000 years of conversation, sometimes serene, sometimes contentious, about the extent and limits of what can be derived from this single source (the Apostles' teaching.)
We apply what Pope Benedict XVI called the "Hermeneutic of Continuity" --- we're looking for those teachings which are directly taught or reasonably inferred (maybe, logically demanded) from the faith of the whole Church from the earliest centuries, as knowable from writings as well as from practice, e.g. Sacred Liturgy.
Realize that every person in the Church has the authority, and of course the duty, to "Obey God rather than men."
So, cut to the chase, how would I, non-cleric, non-scholar, pew-sitter Catholic, react if the pope, professing some level of authority, proclaimed something that was a departure, a rupture, from what we know Christ taught us through the Church an ages past? What if he said Jesus Christ is not God; or man is but a brute, a mutant ape; or Christian marriage makes no durable bond; or intentionally killing an innocent human being is not murder? (My husband and I have discussed this)
I would conclude one of the following:
Under no circumstances (God aiding me) would I conclude that this deranged papal pronouncement was an authoritative teaching--- no, not even if every bishop in the world concurred with it.
Of interest: John Henry Newman's "Development of Doctrine," which invokes internal consistency/continuity as the way to tell true development from either corruption or innovation.
For your amusement and edification: How to Explain Papal Infallibility in Two Minutes (YouTube Link)