This psalm is a twin to Psalm 14 but it is not an identical twin. 

The Psalms go separate ways in Psalm 14:5-6 and Psalm 53:5. I will argue that there is a slightly different emphasis in these psalms and that both fit into different contexts. 

One example that I do not point out on the podcast is that both Psalms use a Hebrew word that means shame.  The word is used in Psalm 14:6 to describe how the wicked seek to shame the afflicted but the LORD will be the refuge of the afflicted. Psalm 14 stresses the deliverance of the righteous. Psalm 53:5 uses the same term about how God will put to shame those who rejected Him. God judges the wicked in Psalm 53.