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Synthetic gear oil from any number of reputable manufacturers is an excellent product. I believe (chemist, retired) it is a better product than standard gear oil. In my opinion it does reduce friction because the number of long chain hydrocarbons is much greater.
Because I own so many vehicles and maintain all of them myself, I always use the lubricants that can go a long time between changes. Synthetics fit that requirement even though they are more expensive. I believe Toyota uses synthetic in their differentials to reduce friction which increases durability.
I believe there are only a few refiners that produce synthetic oils and lubricants. A friend of mine works for a Chevron lube plant and they receive it by rail car. I'm not even sure they add much in the way of friction modifiers.