In an earlier post I noted that the well-educated in the Middle Ages were usually the most intensely religious. Ordinary people would also consider themselves good Christians, but they would not get hung up on fine points of theology.
From the twelfth century on, the elite and ordinary people probably differed most markedly on how to decide if someone was a saint. This was the period in which, for the organized church, becoming a saint was a regular process, requiring well-documented post-mortem miracles. But an awful lot of people still figured that they knew a saint when they saw one.
This can be seen most clearly with the holy greyhound, Saint Guinefort. The story was that some parents had left their baby in its cradle while running errands, leaving the faithful dog (Guinefort) to guard it. (Sounds like the beginning of a good urban legend, doesn't it.) Coming back a few hours later, they found the cradle empty and the dog's mouth all bloody. Horrified, they immediately chopped off the dog's head. Only then did they notice the body of the dead wolf/snake/boar (choose one), killed by the faithful dog, or find the perfectly intact baby in the corner, where it had been thrown during the fight between Guinefort and the terrible monster. Sorrowfully, the parents buried the brave dog.
From then on, Guinefort became a healer of children in his region. Parents would bring sick babies to his tomb, hoping for a miracle. A further refinement was that Guinefort would restore changelings. That is, many a parent decided that a colicky, whiny, failing to thrive, unloveable child was not their real baby. They would bring it to Guinefort's tomb and go away for a short while. When they returned, the saint would have persuaded the elves/fairies/demons to take back the ersatz child and restore the real baby.
This of course sounds very weird to us. But it was all according to normal medieval views of saints, except for the detail of Guinefort being a greyhound instead of a person. Little offerings were still being made at his tomb into the twentieth century.
It is worth noting that no one was declared a heretic for honoring Saint Guinefort. The organized church had far better things to do than to worry about the religious experiences of peasants, as long as they more or less kept in line. They did however try to persuade the followers of Guinefort that they were mistaken, that Guinefort was really a person, not a dog, since dogs did not have immortal souls. This had no effect whatsoever. (See more here on dogs in the Middle Ages.)