Upvote:0
In the Christian tradition, the "Holy Spirit" refers specifically to the "advocate" Jesus promises God will send to his followers after Jesus' crucifixion, see John 14:26.
While it seemingly makes sense to equate the Holy Spirit with the Old Testament manifestations of God's presence, I assume the neither the Catholics nor the Jews who prepared the paper you quote wanted to make a leap of that magnitude.
Upvote:2
One Theory: It's possible that the Jews (which Jews? There's not just one body of "orthodox" Jews.) do not wish to endorse the Christian idea of the Trinity. The Holy Spirit is not exactly described as a divine person in the OT. "Spirit" and "Spirit of God" are used, but not really in the same sense as "Holy Spirit" is used in the NT.
Perhaps alluding to the Holy Spirit is not a concession that the Jews wish to make, and for the sake of expressing positive things in common, "Divine Providence" was something both groups could agree on.
Upvote:2
To answer the O.P.’s question directly, there is no ontological difference between Divine Providence and the Holy Spirit. God (or, if you will, the Divine Essence) is identical with His attributes—including Providence—and also with each one of the Persons. (The best exposition of this idea is St. Thomas Aquinas’ Summa theolgia, I, q. 3, a. 3; and I, q. 39, a. 1.)
I expect, however, that “Holy Spirit” was not used because Jews in general do not, of course, accept the dogma of the Holy Trinity, and “Holy Spirit” in Catholic theology specifically refers to the Third Person of the Trinity. In order to achieve a consensus, a term acceptable to both parties in the joint statement was used.