I may be wrong, but I believe the Vatican gave over to Solesmes the task of producing all official chant books in the early 20th century. So the official Graduale Romanum for the Ordinary Form is that by Solesmes which is only available in book form. The Graduale Triplex is the exact same book, with the neumes of the St. Gall and Laon manuscripts added. The Gregorian Missal (which is online) contains only the chants for Sundays and major feasts, but has English translations, and is drawn from the Graduale Romanum.

Of course, in all of these, the chants have been redistributed for the Ordinary Form, but the music itself has not been edited since the early 20th century - which is why Vatican II called for a new "more critical edition" of the Graduale, still unfulfilled.

The soon-to-be released Graduale from the German scholars that people have been mentioning will be published in Rome, but does not seem like it will be an official chant book for the Church - just used for study purposes - at this point. But it might hopefully advance the cause of the new "more critical edition" from the Church, i.e. Solesmes....?

Do I have that right?

To the best of my knowledge (and if I am wrong I will gladly stand corrected), the official book with the chants for the Mass in the OF is the Ordo Cantus Missae, which only includes a few chants themselves (those that were not to be found in previous official publications), but, whenever possible, simply makes reference to the 1908 Editio Vaticana and its supplements published later. None of these official books includes rhythmic marks.

The 1974 Graduale is a private edition of Solesmes, based upon the 1908 Editio Vaticana with superimposed rhythmic signs, and does not even include all chants mentioned in the Ordo Cantus Missae, since it ommits neo-gregorian melodies whenever possible.

The Graduale Triplex is (as already said above) the 1974 Graduale to which the neums of St. Gall and Laon were added, and is not available online.

The most recent complete Gradual available online is the 1961 edition for the EF, available in this very site, and with rhythmic signs.

The Graduale de Dominicis et Festis about to be published is, as far as I know, another private edition for the OF, not based upon the 1908 Editio Vaticana but rather upon the work of Rupert Fischer et alii. Actually at Gregor und Taube (a German site) you can find most of the chants for the OF, according to the said publications of Fischer et alii, with St. Gall neums above the scores (and a German translation of the Latin, perhaps not very useful for most English speakers). So in a way you can find there online much of what you may want from the Triplex or from the said new Graduale de Dominicis et Festis.

There are proper chants indicated in the section of the Ordo Cantus Missae titled "Cantus Gradualis Romani (Edit 1908) Qui Ad Libitum Servari Possunt" which are omitted from the Solesmes books. E.g., the propers for St. John Cantius.

The OCM is an index that references the 1908 GR, but also includes a number of additional chants (~40). It indicates all of the chants of the OF Mass. The GR1974 is a compilation of the chants based on the OCM, but omitting certain ad libitum chants according to the antiquarian biases of Solesmes. Therefore, one would not err by following GR1974, but would simply miss out on certain options.

Yes, it's similar. But GN is a collection of real neumes from several places, not a production of one set of neumes by averaging them all out and adding a few helpful things. Every neume in GN is authentic, but that's not necessarily the case in GuT.
awr

I suppose there is a task to be done, of comparing the OCM and the GR74 to catalog the differences.

We have at least one indication from the editors on page 8 of the GR74: they added a footnote to the Praenotanda, where the text mentions "neo-gregorian imitations" that one may still sing if one wishes: "Their melodies have been omitted in this private edition."