To answer your question –
There is a difference between Shaul and David:Shaul, of the Tribe of Benjamin, was “chosen” only as a concession to the demand for a king “that we may be like all other nations” 1 Samuel 8.18-20; whereas, David, of the Tribe of Judah was chosen in fulfillment of prophesy – “The Septre shall not depart from Judah….” – because the Tanak describes David as “a man after the heart of HaShem” – David himself said, “…for He has chosen Judah to be prince….” 1 Chronicles 28.4
David is described as a “prince” and “servant” of HaShem – meaning that when klal Yisrael accepts the Davidic monarchy, HaShem will once again be their Ruler and the Kingdom governed by David their “prince” – Ezekiel 34.24:
“And I the L-RD will be their G-D, and My servant David prince among them; I the L-RD have spoken.”
When Am Yisrael demanded a king that “we may be like all other nations” they rejected HaShem’s Sovereignty – 1 Samuel 8.7:
“And the L-RD said unto Samuel: ‘Hearken unto the voice of the people in all that they say unto thee; for they have not rejected thee, but they have rejected Me, that I should not be king over them.”
The distinction between David and Shaul is clear: All of Yisrael followed David with one heart as they recognized that David, as HaShem’s servant drew them near to HaShem [for Worship]; whereas Shaul rebelled against HaShem: “For rebellion is as the sin of witchcraft, And stubbornness is as idolatry and teraphim. Because thou hast rejected the word of the L-RD, He hath also rejected thee from being king.” 1 Samuel 15.23
HaShem’s Torah is contrary to Democracy which is a concept “foreign” to Judaism – HaShem does not want Israel to “be like all other nations” but rather desires Israel to be unique, a “holy nation” as HaShem chose Israel “sui generis” out of all nations to be His servant…. He gave them a “unique” calendar to reflect His Sovereignty over all of Creation – (“This shall be the beginning of months for you”) that Am Yisrael, (led by a monarch in submission to the Torah: Devarim 17.18,19) would be a witness (with one heart) “here on earth” – Shaul’s monarchy was a divided rebellious monarchy whereas David’s united monarchy was in submission to HaShem.
Anyways, I hope you have a wonderful, joyous Sukkot.
Yochanan Ezra ben Avraham