From Immigration Cook Islands:
The Cook Islands does not issue Visas under any circumstances.
For most travellers to the Cook Island, what is generally required is either an entry permit or an exemption from the requirement for an entry permit.
Why does the Cook Islands issue entry permits, not visas? Is it to do with it being in free association with New Zealand?
As a rule of thumb, visas are issued by independent states, while subnational entities issue entry permits. Also, as another rule of thumb, a visa is granted in advance but an entry permit is given on arrival.
The Cook Islands are a dependency of New Zealand that control their own immigration (hence the entry permits), but "outsource" their foreign policy to New Zealand and thus operate no overseas embassies that could grant visas. The vast majority of visitors also receive their permits on arrival, although there is a provision to apply in advance for longer stays/work permits.
Some other examples of subnational entry permits: Andaman and Nicobar Islands (India), Mount Athos (Greece), Sarawak (Malaysia)...
