Depending on how deep the scratch is it may blend back into the stone over time or require re-thermaling. We will often see patios that go in and have a piece or two accidentally scratched that fades into the rest of the stone over time. It ultimately will depend on the material and finish though. Hope that is helpful!
Bluestone is a stone that is native to the Pennsylvania region and is one of the most popular natural stone products in the U.S. in a number of different applications. Flagstone is a broader term that can refer to pretty much any type of stone that is used in a patio. I hope this helped!