I'm sure chonak can identify more completely / accurately, but there are different versions of certain Latin hymns as well as the psalter, depending on the publication year and original reference.
LU has dulces clavos - that is the older Latin version between the two. Not a discrepancy, a different construction of the Latin usage.
This happens from time to time - for example, composers from the 16th century would have used slightly different text for certain motets than what we would see in our "older" version.
I think I have the main of it figured out here, but there are surely some things I'm missing. Crux fidelis is a strophe from a longer hymn by Venantius Fortunatus, "Pange, lingua, gloriosi...certaminis." There are three revisions of the hymn that are fairly widespread.
One begins "Pange, lingua, gloriosi Praelium certaminis." This is the older version found in the Monastic office and in the 1908 Vatican edition Gradual on Good Friday. This is the "dulces clavos" version—or one of them.
Another starts "Pange, lingua, gloriosi proelium certaminis." This is the version in everything post 1970, the same for Good Friday and in the Liturgy of the Hours. It is a slightly revised version of the original, e.g., "dulci clavo."
The other begins "Pange, lingua, gloriosi Lauream certaminis." This is a revision that dates to the 17th century, and is in older Breviaries (pre 1970) and the 1955 Holy Week (Libers and Graduals from the 50s-60s, Parish Book of Chant). Confusingly, for Good Friday, the verses are all from this revision, but the refrain "Crux fidelis" is like 1908 Gradual. So it is also "dulces clavos"... though all the other verses are pretty different. The 1961 Gradual prints in full both the revised verses, and the older version from the 1908 Gradual.
More or less as rarty describes. Pope Urban the 8th thought it was a great idea to have Jesuits alter a large number of the hymns, many penned by saints, because they weren't "as Cicero would have written them".
It gets real exciting when you have a choir of people singing from different books.
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