I'm not sure, but in my opinion there is no difference unless you want to sour the milk before using to increase sodium lactate content. You can't sour pasteurized milk - it just gets rank.
Soapmakerman sours his whole, unpasteurized goats milk for this reason.
You don't need to sour the milk to get all the benefits of a milk soap, Sodium lactate simply makes the bars harder faster, and also makes HP soap pour easier.