Islamic scholars generally agree that the Zabur mentioned in the Quran refers to the Psalms of David. However, a key distinction arises regarding the text's current form. Mainstream Islamic theology teaches that previous scriptures (like the Torah and Gospel) have undergone tahrif (alteration or corruption) over centuries. Consequently, many Muslims believe that while the current Book of Psalms contains the remnants of the original divine message, it also contains human additions and alterations.
Here’s the key distinction:
To give a full answer, we cannot just say "Islam." We must look at three Abrahamic faiths.