I'm a little confused by what you mean by direct eppler to NACA equivalence as well. They are not the same any more than a Quabek has any equivalence to Eppler or to NACA airfoils other than how they share the concepts of camber and envelope profile.

The 4 and 5 digit series NACA airfoils are symetrical shapes made using mathematical formula that are then bent around camber lines to form the shapes. Alternately the modern shapes are designed using flow analysis to shape the airfoils around some basic values that set the thickness and camber.