The occipital pull chin cup is frequently used to treat:
Types of Chin Cup

Occipital pull chin cup derives anchorage from the occiput region. This is used in Class III cases with mild to moderate mandibular prognathism, who can bring their incisors in an edge-to-edge position at centric relation. Patients with short anterior facial height also benefit from this type of chin cup. This is the more commonly used chin cup.
Vertical pull chin cup derives anchorage from the parietal region. It is indicated in high angle cases or long face patients, as it helps to close the angle of the mandible and increase the posterior facial height.

Ref: Textbook of Orthodontics Gurkeerat Singh Second edition
Maxillary prognathism
Mild to moderate mandibular prognathism
Class I skeletal cases
Class II skeletal cases