From the Super Mario Wiki
Peaches are edible, juicy fruit with restorative properties. Peaches have become a symbol of Princess Peach as a result of her use as an emblem for her band, the Peach Hit Five in Super Princess Peach.
Although Peachy Peaches have a similar name and appear nearly identical, Peachy Peaches are actually created through human means, while peaches grow on trees.
Super Smash Bros. Brawl
In this world, Peaches appear during Peach's Final Smash, the Peach Blossom. The move puts all of Peach's enemies to sleep while normal-sized peaches fall from the sky. Because of the state of her opponents, Peach is free to consume all of the peaches and restore her health. However, if she isn't quick enough or her attack misses, her opponents are able to eat the peaches as well.