It is due to different translations of the Bible.  The psalm in the prayers at the foot of the altar used the Vulgate translation whilst the introit is from the Vetus Latin/Italica text.

Pope Pius XII introduced a new translation of the Vulgate that ... everybody hated and nobody ended up using.  Not only did it ruin the rythm of the chanted Psalms that nearly all religious orders used, but IMO the Latin was very stilted, and anyone who's gotten used to the traditional Vulgate translation would not take to it well.  I very much disliked it myself.

I agree, I'm sad he did that. 

The more you know! I didn't realize that and I've probably sung through the entire liturgical year save for one or two Sundays

I would need to look this up for this specific case.

Neverthess, apart from the lections using the Vulgate, most often the Mass uses the Latin version found in the Vetus Latina, not the Vulgate.

This is why we pray:  Gloria in EXCELSIS Dei...

Not:  Gloria in ALTISSIMIS Deo...

I found the stated intent of the New Psalms (and then Vulgate) translation to be suspect of Modernism.

New Latin Version of Psalms (1945):

Pope Pius XII commissioned a new Latin version of the Psalms, prepared by professors at the Pontifical Biblical Institute in Rome, for use in the Divine Office. This new translation aimed to be closer to the original Hebrew text while still maintaining the tradition of the Vulgate

"Closer to origina[sic] Hebrew test":  Hebrew text has been manipulated to remove or water down obvious Messianic references to Our Lord.  Septuagint and St. Jerome's Vulgate are most certainly better reflections of the original Hebrew, AND not only were the translators of Septuagint experts in both Hebrew and Greek (which were for them living languages), St. Jerome was also fluent in Greek and Latin and very adept with the Hebrew.  So I'll take their understanding / interpretation of what the "original" Hebrew text actually meant over that of some modern "scholars".  And then there was room (as there is in every translation) to put Modernist spins on texts by subtle variations in the translation.

Given the Modernist-infested climate of the 1940s ... I'll say a firm "no thank you" to this translation.

But I resent the implicatoin that modern scholars are "smarter" than the great minds (often saints) who made the original translations, especially since St. Jerome was in the Patristic era where they also had a very strong living Tradition of the APOSTOLIC interpretation of Sacred Scripture to apply to the translators.

Consequently, this new translation = total garbage.

That's to say nothing of how the new Latin Psalms clashed with the traditional Gregorian melodies.

Was it his fault? They did away with his changes to the latin, or did they miss that one?

Hard to know.  Pius XII was enamored with modern "science" and "scholarship" ... to a fault, but at the same time after his health collapsed in about 1954, I doubt he was actually running much of anything.