I'm confused... Is there a simple answer defining the differences between the two class's?
AS far as I understand it LMdH is taking over from DPI, with only choice of 4 chassis, + common gearbox and hybrid system. LMH (ot hypercars) takes over from LMP1, and is a pure prototype category. LMdH using standard components would be cheaper: Porsche and Audi chose that path. LMH has more freedom of design; Toyota, Glickenhaus and ByKolles , plus possibly Peugeot. There will be BoP to equalise both categories.
User @lmpdesigner has a very deep knowledge about the two classes and also all the politics involved (as LMH is kind of an "accident" in my opinion as the previous involved manufacturers who voted and pushed for LMH pulled out)