Basiclly. Div 1 is a "concervative way to design" a pressure vessel based by rule (following equations).
Div 2, is a alternative way to design a pressure vessel, in a more "Economical" point of view; regarding with the requeried material thickness: you will get less material thickness, but the material inspection is more hard and more demanding than Div 1, as well Div 2 allow you to design by "stress analysis" using a FEA software for example (appendix 4), so design by analysis is allowed.
Div 1 and Div 2 uses diferent values os "allowble stress" due to the fact of the nature of the assumption taken during their formulation.
hopping that will help you a little bit.