Despite being a very exploration based game, Super Mario Odyssey has a lot of story related moons that feel similar to the stars from Super Mario Galaxy’s mission based format. These moons are on a special pedestal, and they are sometimes even three moons in one! If you still aren’t sure what these are, just think of them as the moons that get a special animation when collected that ends in a zoom-in on Mario and Cappy separated.
This walkthrough showed me the moon names, but still let me know in the comments if any are wrong: https://gamefaqs.gamespot.com/switch/200275-super-mario-odyssey/faqs/75302
This quiz won’t include Mushroom Kingdom, Dark Side, or Darker Side moons. These don’t show up until after you beat the game, so I can’t really call them “story” moons. You don’t technically have to collect some of the moons on this quiz anyway, but they are all plot related.
Cap Kingdom, Cloud Kingdom, Lost Kingdom, and Moon Kingdom are part of the main story, but don’t actually have main story moons, so they won’t be here.