Synthetic and regular engine oils are completely compatible and can be combined without causing problems, as long as the engine is compatible with synthetic oil. Both synthetic and regular oils are refined from crude oil.
Synthetic oils are not fake. They have gone through a process to make the molecules the same size for better lubricating properties. Some of these processes make large designer molecules from smaller molecules. Some of these go through a process that breaks down and rearranges larger molecules into designer ones.
Full synthetic oils also have additives designed to improve performance. Some of these enhancements include an increase to film strength and a higher temperature threshold.