only on the list
The caption on a place in the list shows up only on that list. The reasoning behind that is that if you’re writing about a place on the “Best chocolate cake” list, it might not necessarily make sense to show it on a “Best burgers” list if the place is also on that list. In the future, list captions might also show up on the individual place page.
By the way, if the list owner sets the “can community members contribute”, anyone can edit captions. Otherwise, only the list owner can.