The first one, if done competently, can always be played comically or dramatically. The second kind -- well, it depends. Most of the stories set in a land where fairy tales are true are set in land where only a small handful of the best known tales come true, and keep on doing it furiously all the time.
Not unnaturally, this leads to stories where characters are always trying to exploit or subvert the standard fairy tale tropes to a comic extent. Widowers don't remarry, or if they do, their wise second wives go out of their way to be nice to the stepdaughter. The older two sons point out to their father that they are bound to fail so the youngest son should go first. And people would be very, very, very careful what they wished. You get tales like Patricia C. Wrede's Enchanted Forest Chronicles, in which one princess laments that an evil fairy came to her christening, and her families succeeded in appeasing her, which kept her from cursing the princess, and while many princesses manage without such a curse, that's when the evil fairy didn't show up. In Howl's Moving Castle, Sophie "knows" that as the oldest child, she's bound to fail worst at finding her fortune. Terry Pratchett pushed it farther in Witches Aboard, where the magic forces people into patterns, as best it can, and things keep bursting out of it
Though I suppose it could work if the fairy tales were peppered throughout history; it's the relentless recurrence that clues people in. In John Barnes's One for the Morning Glory, they know the tale of Sleeping Beauty as history, but it's sole appearance is an explanation that they do not know when and where they are in the tale, so they do not know how the tale ends, and whether their own deaths work in it. If it were just a bit of back story that even though Queen Aurora Rose lived two hundred years ago, people still remember the vital importance of inviting all fairies who wished to be invited, and so even a merchant's daughter like Cinderella had one if the fairy godmother was interested.
If someone did it. Most writers who managed a dramatic treatment don't. Instead they opt for a plethora of fairy tales. After all, if you have three sons, you don't have to send them all on a quest for the first two to fail and the third to succeed; you could be in "Mollie Whuppie" and need only wait until the heroine shows up with her two sisters, and you can bribe her with a wedding each time you want to send her back to steal something from the ogre, and then you have your three sons neatly married off to her and her two sisters. Burning the skin of your shape-shifting lover might win you a permanent change to human form -- or send you off on a long quest to recover your true love. Not remarrying might spare your children a wicked stepmother, but might mean you fall madly in love with your own daughter, or that your older daughters would take the place of the wicked stepmother in abusing the youngest. No Rest For the Wicked manages to keep matters serious by its masses of fairy tales, which means you can't predict what will happen if you do something.