Salamun Alaikum,
*Shara'a - is to ordain, to enact a law, to lay down the law. Shariah therefore is an ordained way. See 45:18.
For example, they leave God's ordained religion and succumb to man-made 'shariah' (man-made ways) which God has not ordained. In doing so, they set up partners / rivals with God.
042:021
“Or have they partners who have ordained (Arabic sharaa'u*) for them in religion that which God has not allowed? And if it was not for a decisive word, surely it would have been judged between them. And indeed! for wrong-doers is a painful doom”
So the Shariah from the Quran is God's law that has been ordained for believers.
Once a law is defined, then the road or way becomes apparent. This is described as ‘minhaaj’ (open way / manifest road). Then one follows the laws or follows a road, makes a way, traces or broadens. It is like a path or an open road where such laws are followed.
So each people had their laws (Shariah) made apparent to them / and their open ways (minhaaj). They were expected to apply them to their conditions with a view to race to good and to get closer to God.
I hope that helps, God willing.
Joseph.