If you were to look at some of the dark patches of the moon it resembles an image of a rabbit working a mortar and pestle. The story of that originated from China and some variations of it has spread around to the other neighbouring countries.
The story goes that there’s a rabbit that serves under the goddess of the moon and is pounding the elixir of life for the other immortals. Japanese and Korean versions replaces the elixir with mochi or rice cakes based on the Shinto beliefs.
Thailand and Vietnam have a different story for the rabbit which originated from the Buddhist Jataka Tales. It tells the story of Buddha, in disguise as a beggar, was so moved by the self sacrifice of the rabbit’s generosity to offer itself as the beggar’s food that he drew the likeness of the rabbit on the moon for all to see. In that version the silhouette of the rabbit is flying over the smoke of a cookery pot.