Parents passed down the stories to their children. Later, people collected the stories and wrote them down. There was some editing in the writing down. There could have been many versions of Little Red Riding hood in the verbal telling. I found it fascinating reading the different written versions of well-known stories.
All stories evolve and change with time and place.
Here are reference sites to help you understand the strange but wonderful world of myth and folklore. Folklore and Mythology Electronic Text Pick a topic like animal brides, or multiple births or werewolves and read the tales on the Folklore and Mythology Electronic Text. There are 11 water spirit stories from Russia, Germany and England. Traveler's folklore has 10 entries from England, Japan, North America, India and Romania. A great way to compare stories, globally.