I guess in the sense that these were all originally fairy tales, a compilation of them must also be a fairy tale? Many details are left that would not coincide with the new story that is being formed with all of the characters in Fables, such as Snow White's evil stepmother or the seven dwarfs. That is made to be part of her past, so that instead of combining the fairy tales, they just use the characters to form another fairy tale that presumably occurs after the events of the original tales.
Into the Woods, on the other hand, more or less maintained the actions of the original tales, but had the characters interact with each other in the infamous forest that many stories use. Cinderella is still trying to get to the ball despite her stepmother and stepsisters and Red Riding Hood is still trying to get to her grandmother's house.
In a way, Into the Woods is more like a traditional fairy tale than Fables because it maintains the separate story lines, and Fables is a mystery, which is not typical for fairy tales. There is not a great deal of magic in Fables, and it feels more like "a day in the life of a fairy tale character." Though they both combine elements of well-known fairy tales, the end products are not the same.