There is no such thing as "normal" synthetic oil. Synthetic oil is made from non-petroleum base compounds. If you remember chemistry, crude oil is processed to create diesel, petrol, aero-fuel, bitumen and others. Part of that is "mineral oil".
Synthetic oil is completely man-made via chemical processing. I do not understand enough to explain it but it sounds really complicated. It was created during World War 2 by scientists as getting fuel for the war machines tend to be a problem during war time.
There are big advantages for using synthetic oil in performance cars. However, https://www.mobiloil.com/USA-English/MotorOil/Car_Care/AskMobil/Mobil1_Mazda_Rotary_Engine.aspx
I use the cheapest mineral oil I can find within the 15W to 50 range. I can actually think of a few reasons to use synthetic in a rotary but since it was not recommended by experts, I just dont. That and I am on an FC, not much performance gain using synthetic in the old 13B engines except for the speed of the cash flying out of my wallet.
[EDIT] I stand corrected, Idemitsu DOES make a fully synthetic rotary oil. But when I saw the price... haha... I think I'll stick to my Castrol GTX and other cheap lube.