Zabur names the scripture revealed to David. In Arabic, one use of the root z-b-r is “to write,” which supports the explanation of Zabur as something written or recorded.
The linguistic explanation is useful, but the central point is that David received divine revelation.
Thus the Torah, Gospel and Psalms have different names and linguistic backgrounds while their original revelatory source is divine. Variety of names does not imply a variety of ultimate sources.