Theory: Power Moons and Shine Sprites and Power Stars

Abstract
Power Moons and Shine Sprites are the same things as Power Stars, just in different shapes.

Arguments

 * Argument 1: There are design elements shared between Power Stars, Power Moons and Shine Sprites. They have the same eyes, same common coloration, and are all based on celestial bodies (technically the same celestial bodies from different distances in the case of Power Stars and Shine Sprites). Grand Stars (a type of Power Star), Power Moons and Shine Sprites have the same ball-points at their tips. Many of the various colors of Power Moons match the colors of Power Stars and Lumas seen in other games.


 * Argument 2: They are all used as Power Sources. Power Stars can be used to power ships, buildings, machinery, etc. (As seen in Super Mario 64, Mario Party, Super Mario Galaxy, Super Mario Galaxy 2, Super Mario Odyssey, etc.). In Super Mario Odyssey, New Donk City runs on Power Moon energy, as do airships, the robotic bosses and the Steam Gardeners. In Super Mario Sunshine, Shine Sprites are stated to be the source of Power on Isle Delfino. It’s said that their collective power sustains the island and provides its energy.


 * Argument 3: Both Power Stars and Power Moons have liquid-like energy forms that can be used as fuel for things like machinery and ships.


 * Argument 4: Power Stars and Power Moons can also both be used to fix and change the appearance of ships, such as the ones that became Starship Mario and the Odyssey, respectively.


 * Argument 5: Shine Sprites, Power Stars and Power Moons all naturally float. They all produce great amounts of light and have extremely similar glows.


 * Argument 6: When Cappy first sees a Power Star in the Mushroom Kingdom in Super Mario Odyssey, Cappy states that Power Stars and Power Moons (the Power Source he’s familiar with from his home) are the same things in different shapes.


 * Argument 7: At the beginning of Super Mario Sunshine, when Toadsworth first sees a Shine Sprite, he compares it to a Power Star, but notes that it isn’t (likely because of the different shape).


 * Argument 8: The shapes of Power Stars, Moons and Shine Sprites appear on pillars and ruins of buildings surrounding the Rainbow Coaster from Mario Kart Arcade GP.


 * Argument 9: Manhole Covers on Isle Delfino depict abstract art of Shine Sprites, but also art in the same abstract style featuring a crescent moon with a similar shape and face, perhaps representing Power Moons. The similar style in the art as well as shared crowns establish a connection between the two.