both psalms 14 and 53 were written by David, while psalms 53 was coauthored Korah, psalms 14 was a part of the first 41 chapter, called book one. while 42 to 72 was book 2,
it is suggested that book 1 was compiled by David, book 2 was compiled by either Hezekiah, or Josiah.
and they were compiled in 2 different time periods.
apparently David felt so strongly about the godlessness of the people that He wrote almost the same psalm twice, and sent them to two different choir directors.
it is not uncommon to see the same thing written in different parts of the bible, that was Gods way of emphasizing what was important to Him.
you will find almost the same wording in 1 Peter 2;23, as in Isiah 53;5,
if it is important for us to learn something in the bible you will find it 3 times.
Exposition of Psalm 53. – Charles H. Spurgeon
TITLE. To the Chief Musician. If the leader of the choir is privileged to sing the jubilates of divine grace, he must not disdain to chant the miseries of human depravity. This is the second time he has had the same Psalm entrusted to him (see Psalm 14.), and he must, therefore, be the more careful in singing it. Upon Mahalath. Here the tune is chosen for the musician, probably some mournfully solemn air; or perhaps a musical instrument is here indicated, and the master of the choir is requested to make it the prominent instrument in the orchestra; at any rate, this is a direction not found in the former copy of the Psalm, and seems to call for greater care. The word “Mahalath” appears to signify, in some forms of it, “disease, “and truly this Psalm is THE SONG OF MAN’S DISEASE— the mortal, hereditary taint of sin. Maschil. This is a second additional note not found in Psalm 14, indicating that double attention is to be given to this most instructive song. A Psalm of David. It is not a copy of the fourteenth Psalm, emended and revised by a foreign hand; it is another edition by the same author, emphasised in certain parts, and rewritten for another purpose.
SUBJECT. The evil nature of man is here brought before our view a second time, in almost the same inspired words. All repetitions are not vain repetitions. We are slow to learn, and need line upon line. David after a long life, found men no better than they were in his youth. Holy Writ never repeats itself needlessly, there is good cause for the second copy of this Psalm; let us read it with more profound attention than before. If our age has advanced from fourteen to fifty-three, we shall find the doctrine of this Psalm more evident than in our youth. The reader is requested to peruse Psalm 14, “Treasury of David, “Vol. 1.