The story about the dog who sees his reflection in a lake, thinks it's another dog, then drops his bone in the water trying to snatch the reflected bone, is allegorical. Allegorical means containing a moral or hidden meaning.
Allegorical stories and plays use concrete ideas as symbols for deeper or layered meanings. Folk tales and fables are often allegorical. Visual art, like paintings, can also be allegorical, with religious or even political messages symbolized by painted figures. The Greek word for allegory, allegoria, comes from allos, "another," and agoreuein, "speak openly. So if you speak of one thing, but mean something else, that's allegorical.