GIRM 61. ... The Responsorial Psalm should correspond to each reading and should usually be taken from the Lectionary. It is preferable for the Responsorial Psalm to be sung, at least as far as the people’s response is concerned. Hence the psalmist, or cantor of the Psalm, sings the Psalm verses at the ambo or another suitable place, ... [common psalms, in lectionary ≈ GS] ...
Instead of the Psalm assigned in the Lectionary, there may be sung either the Responsorial Gradual from the Graduale Romanum, or the Responsorial Psalm or the Alleluia Psalm from the Graduale Simplex, as described in these books.

So 1/ Lectionary, for the day
2/ Lectionary appendix common psalm
3/ GR
4/ GS

The Latin Mass that is governed by TC is the preconciliar Latin Mass. Latin Masses celebrated in accordance with the current typical edition of the Missale Romanum (where the entrance/offertory/communion chants are included, not in the Lectionary) are not governed by TC.

By Flowing Waters (Paul F Ford) translates GS into chant in English. If I am correct in thinking that they are the same as the common psalms, the difference is just singing verses or stanzas, BFW congregations get twice as many responds.
I have never encountered a Responsorial Psalm (as in the lectionary) in Latin and would not wish to do so. I agree with the view that the liturgy of the word should be in the vernacular, where such exists, or in a lingua franca, and have espoused that since 1965 when the TLM was first modified in the light of SC (and Trent XXII: viii).

There were ICEL translated, and SCR/CDW appproved, translations of GS antiphons.

Our bishop has (unfortunately) been on the firmer side of crackdowns, but this has nothing to do with the Novus Ordo since TC was aimed only at tridentine celebrations. TC has nothing to do with the N.O. in Latin.

It's just a bad translation of Responsorium Graduale: I would have said "Gradual Responsory" (since the Gradual is, in fact, a Responsory, even if the respond isn't usually repeated after the verse). But the real problem is that the Ordo Cantus Missae that the 1974 Graduale Romanum is based on doesn't only have Graduals after the First Reading: Eastertide has the First Alleluia; Palm Sunday and Good Friday both have the Tract after the First Reading (with the Grad. Christus factus est before the Gospel); and Trinity Sunday has the Canticle of the Three Children from the former Ember Day Mass as an alternative chant to the Gradual: someone who is truly rigid (pace Bergoglio) could interpret the GIRM as permitting the Gradual from the 1974 Graduale Romanum, but not the other interlectional chants in the same book.

Also this is another example of the "Treasury of Gregorian Chant" allegedly "a treasure of inestimable value" being officially relegated to the dustbin of history. The Graduals and Alleluias are the most glorious chants in the entire Graduale Romanum, but what we get instead is musical gibberish. I realize that this may hurt people's feelings, but I have yet to come across ANY settings of the Responsorial Psalms from the Lectionary that are little more than utility music: even the best pseudo-chant settings are usually banal, and I include my own settings in that heap of forgettable ditties.

Edit: lmassery's comment posted while I was typing this, so please note that it is in no relation to the file that he uploaded: this is an addendum to my own previous comment.