Well, without having read the 'la luna short story' it's hard to say for certain. However, generally speaking, it could be about the cultural significance of the moon in a particular community. It could explore how the moon affects the daily lives, beliefs, and traditions of the people in the story. Maybe it's a story of a family that passes down stories about the moon from one generation to another, and these stories hold some kind of important meaning or lesson.
The main characters in the 'la luna short story' could be a diverse group. There might be an old storyteller who shares tales about the moon. And perhaps a group of children who listen to these stories and are then inspired to go on their own adventure related to the moon. There could also be a character who is a bit of an outcast in the community but finds solace in looking at the moon.
The main differences could lie in the way the story is presented visually, or maybe in some character developments. Sometimes the anime might add or omit certain plot points for better pacing or to suit the animation format. However, it's hard to say exactly without specific details about the 'ooh la la manga'.
The anime of Kill la Kill debuted earlier. The manga followed later, building on the popularity and story established by the anime. Generally, in this case, the anime led the way.