Before revision:  In the former case, margin valuation adjustment (MVA) is defined as the liability-side discounted expected margin profile, while in the latter, an extended partial differential equation is derived and solved by finite difference for an all-in fair value, decomposable into coherent CVA, FVA and MVA.
After revision:  In the former case, margin valuation adjustment (MVA) is defined as the liability-side discounted expected margin profile, while in the latter, an extended partial differential equation is derived and solved for an all-in fair value, decomposable into coherent CVA, FVA and MVA.