Silver Moon Rings are silver-colored Rings with a crescent moon floating inside of them in their center.
In gameplay, when the player has collected all five Red Star Rings in a stage, then all of the Number Rings in another playthrough of the stage, they will be able to collect Silver Moon Rings in subsequent playthroughs of that stage.
Similar to the Number Rings, all of the Silver Moon Rings are found within a particular section of a stage. However, Silver Rings do not need to be collected in a specific order. Instead, it is requiring that the player grabs them all within a set amount of time after grabbing the first one. If the time limit expires before all five rings in a set are collected, they will vanish, requiring the player to restart the stage from a point before activating them for another chance.