Ecclesia Militans, the blog of a firm adherent of the SSPX, has a piece by the SSPX Fr. Peter Scott (rector of the SSPX seminary in Australia) about the differences between the older form of Mass and the newer form.
He picks up on the terminology of "ordinary" and "extraordinary" use of one Roman Rite.
His comments are interesting and thought provoking and must be treated with due respect.
Here is an excerpt. He is talking about the fact that there is no problem with having more than one Rite. My emphases and comments.
The multiplicity of different forms re-emerged, but much more radically, with the post-conciliar introduction of the novelties and continual changes of the New Mass. The confusion, loss of unity, desacralization is far worse than that involved in the slight variants of the middle ages. Moreover, it cannot be said that these are forms of the same Roman rite as the traditional Mass. [Pay attention: He is reacting to the provision in Summorum Pontificum that the Novus Ordo and the "Vetus Ordo" are two "uses" of the one and same Roman Rite. He disagrees. He is saying that they are different rites.] They are forms of the New Mass. However, to say that the New Mass and the traditional Mass are forms of the same Roman rite would mean to say that they are substantially identical, and that the differences are only accidental. To the contrary, some accidental aspects, such as appearances, are similar. The substance is entirely different, for the traditional Mass is a true, propitiatory sacrifice, the same sacrifice as the Cross offered in an unbloody way to expiate the crimes of sinners. The new Mass, to the contrary, is a banquet, a celebration of the community, a sacrifice of praise and thanksgiving, an acknowledgement of Christ’s love for humanity. [I think he is wrong here. The Novus Ordo also makes it sufficiently clear that what is taking place is the Sacrifice of Calvary. However, he is putting his finger on an important point: the prayers of the Novus Ordo, even when they were taken from ancient sources or the more proximate source of the pre-Conciliar edition of the Missale Romanum, were systematically edited for content. So-called "negative" concepts (emphases on the Four Last Things, guilt for sin, the claims of the Church about herself, etc. were edited out or softened. In there place were inserted other kinds of ideas, in themselves perfectly find, but quite different, such as the need to perform good works as a consequence of receiving Communion, etc. Shift the prayers, and you shift a great deal more in the Church! So, he is one to something that quite a few people are really taking a hard look at.] The meaning of the gestures, symbols, ceremonies and prayers is radically different.
The only way to affirm that the New Mass is the ordinary form and the traditional Mass the extraordinary form is to pretend that there is no fundamental difference. It is to look at the exterior alone, to live in a fantasy world, [This is a bit too tendentious, I think. But not unexpected considering who is talking.] and to pretend that the traditional Mass has none of the doctrinal depth and richness that distinguishes it from the New Mass. [And interesting approach, but not as effective as merely stating that the Novus Ordo simply doesn't point us well-enough to an indispensable dimension of our Catholic faith and something we ignore at our peril.] This is likewise the only way to come up with the preposterous claim that the rite of Mass that has been used constantly in the Roman rite for more than 1500 years has all of a sudden become in some way “extraordinary”. The fact remains that they are two different rites, and that if one claims, as did Benedict XVI, that they should [should] “mutually enrich one another” is to transform the traditional Mass into an entirely new rite, the New Mass. [No, that doesn't at all follow. The older form might slowly be transformed, but not into the Novus Ordo, "the New Mass", but rather something else, a "tertium quid". Also, I am not sure about the "should" part. I think it would be more accurate to say "will". That influence is going on even now, like it or not. It cannot be otherwise.]
Scott has several good points. He rightly exposes that there are different emphases in the prayers of the two forms of Mass. However, I think he slightly overstates his case by not allowing that the Novus Ordo also reveals internally that it too is the Sacrifice and not just Banquet.
However, I think where he stumbles a bit, and this is important for all of us to understand, is that by stating in Summorum Pontificum that there are two uses of one Roman Rite, Benedict has made a juridical distinction. This is critical to understand how Benedict derestricted the older form of Mass so elegantly.
By saying that, considered juridically, there is only one Rite in two uses, Benedict eliminated the need to grant special faculties (canonical "permission to say Mass" coming from proper authority) to say the older Mass. If a faculty can be given, it can be withheld or withdrawn. By saying that there is just one rite, juridically, Benedict has seen to it that if a priest has the faculty to say Mass in the Roman Rite at all, then he has the faculty to say either Mass, the older or newer form or use. This is a juridical distinction.
Benedict is not, I believe, saying that there is no longer a question of whether or not the Novus Ordo is, considered historically, liturgically, theologically, etc., a different Rite. This was an elegant juridical solution.
I think the question remains open about whether or not the Novus Ordo is really a different rite.
Frankly, I think it probably is. I think the changes made were different enough to constitute it as a different rite. I frankly think that that is what Benedict XVI thinks too, based on what I have read and also knowing the great esteem and harmony he has with Klaus Gamber.
A lot more study of this needs to be done and I sincerely think the door is still open for that study. The need is sure there!
That said, I thank His Holiness for the elegant juridical solution in Summorum Pontificum of considering there to be one Roman Rite, juridically considered.