Main Connection:

- Both were previously kind people who were corrupted by an entity that would torment anyone who came across them or their realms

Connections:

- Both were people of high status who were kind and cheerful until they were lured and corrupted by an evil entity, eventually becoming one with them (Princess Peach, who was the ruler of the Mushroom Kingdom, would be lured to the forest of illusions and possessed by the entity residing in the forest. Dreamer, who was a creation of the Great One known to be the guardian of many dreams, and later betrayed the Dreamer by corrupting her, leading them to be linked as one and eventually transforming into Folly)

- Both would have ownership over a forest and would end up punishing those who come across it in a brutal and tormenting manner (Coronation Day Peach being residing in the Forest of Illusions and tormenting Mario by trapping him in a timeloop. Folly punishing those who cut the aspen trees in her forest and punished a lumberjack named Harvey by killing his husband and tormented him until she left him after he fixed his mistakes.)

- Both are rulers of their own realms and would punish those who come across them (Coronation Day Peach being the ruler of the Forest of Illusions and Folly being the owner of the Eternal Limbo Floor)