The word progestin refers to any compound that will maintain the secretory endometrium. It does not infer that a progestin's action is identical to the wide range of actions provided by real progesterone. The word synthetic infers artificial, not found in nature. It is different than the word synthesized which means only that a compound was put together from parts. In our bodies we synthesize hormones from cholesterol.
Commercial progesterone is synthesized from plant fats.
Being identical to endogenous progesterone, it is not synthetic. Our bodies do not synthesize progestins. They are found nowhere in nature. Therefore they are synthetic. There is a difference.