Moon-Shaped World was not an anime. Although the moon-shaped world had some anime elements, it was essentially a fictional novel series from Japan. The series consisted of several novels and comics that told the stories of a group of young people taking risks in a fantasy world. Although the moon-shaped world could be adapted into anime, movies, games, and many other forms of work, it was not an anime itself.
I haven't got any information about the Pakal Nakshatrangal story yet. It could be something very unique and specific to a certain culture or community.
In the search results provided, there was information about anime characters transforming under the moon. Among them, Moon Hare, the protagonist of Sailor Moon, was a spokesperson for the moon. She transformed into the Sailor Moon through the brooch and had the power of love and justice to fight against the dark forces. In addition, the Saiyan in Dragon Ball would transform into a giant gorilla during the full moon, and their strength would increase greatly. These characters had a close relationship with the moon and would transform under the moon.
Overall, there are noticeable differences. The anime might have adapted the plot to fit the animation format, and there could be variations in character designs and the pacing of the story. However, both still retain the core essence of Sailor Moon.
Unable to answer this question because you did not provide any relevant anime characters or context information. Please provide more details or background information so that I can better answer your questions.