Ivy tracks your movement with a 3-axis accelerometer and your heart rate data with an optical heart rate monitor while Leaf uses the 3-axis accelerometer as well but does not have the heart rate monitor.
This means that the Leaf will track your activity and sleep automatically and sync that information with the app once prompted while the Ivy tracks your heart rate data as well. All the information Ivy tracks with the optical heart rate monitor is available through the Readiness screen - heart rate, respiratory rate, resting heart rate and cardiac coherence.
Leaf can be worn in three different ways - as a clip, necklace and as a bracelet, where Ivy can only be worn as a bracelet due to the optical heart rate monitor.