Hmmm ......... I suspect your suspicions on being a repack might turn out to be true. Dupont who own teflon do not sell it to other manufacturers unless they know exactly how it is going to be formulated and they are given a copy of the formulation. When we were working on an aircraft surface finish they were very hand in hand with us, the product did not eventuate. I have to say reviewing the description of the white grease would makes me think it is lithium grease, they don't actually state it contains PTFE, just has the same slippery properties.
The molly base could be from any of a dozen or so different manufactures formulated to perform what ever task the grease is intended for, I have a 2.5 litre tin from castrol, best way to buy it, it will last me forever.
As they say peteski, 'the proof of the pudding is in the eating' it works for you so don't change until there is proven better.