Both means future, but for me Shourai sounds more personal as opposed to Mirai. When I say my Shourai, it's about my future job, my future husband, or something that will happen in my real life. Mirai is used for something more general, like Japan's Mirai, children's Mirai, society's Mirai... Thhis doesn't mean they can't be used interchangeably. But generally, Shourai is used for something personal and realistic. Mirai is more general, possibly unrealistic. For example, mirai no kuruma (future cars), we can only imagine how it will be. We can imagine super futuristic cars with wings or whatever which might happen or might not. Shourai no kuruma sounds more realistic. They won't fly in the air but they might be fully automatic with self-controlled handles & brakes.

I found some of the same questions posted on italki previously. I like the following one; https://www.italki.com/question/193879 You can find others by searching for e.g. "未来　将来 difference".