Well, with saints, the Church has a criteria for sainthood. Over the millenia, the Church has seen some really interesting things with saints. For example, it has noticed that some have bodies which are “incorruptible”…don’t really decay!
Further, when people pray to these individuals, miracles can happen. When the Church can document 2, and the Church is quite strict, the person can be canonized, from my understanding of it.
To be considered a saint, the Church will look at a person’s life, ask a lot of questions, look for other signs…miracles, etc.
Let me give you one case of a saint that comes to mind off the top of my head. We have St. Philip of the Cross. If memory serves, he had to walk something like…500 miles, was crucified with a bunch of others. In the end, they put a lance through his heart. I think he, with the others…SANG on the way to their torture and death!
There were all these bodies on the crosses, and the Japanese, I believe, noticed these bodies did NOT decay like other people’s. They saw all that and believed! I think that entire city was converted due to their martyrdom!
There are some cases that merit canonization. That’s just one of many. The Church has the authority to recognize saints. It’s one of her many gifts.
I can’t really speak to saints in the past, since I simply don’t know how that works so will let someone else address that issue who does.