1. lack (unknown murderer)
2. quest (to find murderer)
3. encounters magical helper (wolf, pig, etc.)
4. tests (eliminating suspects and all the obstacles, ex. stopping the murder of Jack by Bluebeard)
5. reward (well, I guess Snow White got her sister back and she could've had her wolf-prince if she wanted)
Into the Woods definitely appears more like a fairy tale, at least initially. It is spoken in the form of a fairy tale by a storyteller. It relays classic fairy tales in the Grimm tradition and invents its own that follows the same style. Morals are clearly spelled out at the end of each act, and although things totally change after the narrator is eaten, the stories still end in their traditional way (ex. Cinderella's eyes plucked out by birds), so the lack of narration changes the way the story is relayed but not it's content.