The simple t = PR/S for a cylinder is based on thin shell theory, where the shell will be in pure hoop tension.
However as the thickness increases there are additional stresses in the shell plate. The 0.6P term is a simple correction (though not a perfect correction) to account for these. At sufficiently high pressures or shell thicknesses the Appendix 1-2 formula must be used to more completely account for this effect. Division 2 Part 4 uses this more accurate formula for all pressures and thicknesses.