theres nothing specific about synthetic oil, its like saying you have a cabon frame, doenst specidy if it was intended to be a selvet track bike or a 12" hucking freeride monster.
Synthetic just refers to the manufacturing process where the oil is synthesised form other hydrocarbons as opposed to mineral oil which is simply a mixtrue of various crude fractions.
What the oil is used for is more down to its additives. eg gear oil has a high sulphur content and a small ammount of very very long hydrocarbons, these would lead to an almost instant emissions failiure if you ran it in an engine, but does help it survive for 100,000miles between changes in modern car and van gearboxes. Similarly fork oil will have been developed to be as slipperly as possible with the minimum of foaming and to be as newtonian as possible. Somethign stickier is probably usefull in the lowers as you want it to coat the stanchions, but not so sticky that it just clings to the inside of the lowers or actualy creates friction 9remmber gear oil doesnt have to lubricate as much).