Corals and monkeys are both animals and belong to the taxonomic kingdom Animalia. All animals are multicellular creatures, and all animals rely directly or indirectly on other organisms for nourishment.
Although monkeys are more complex creatures than tiny coral polyps, monkeys and corals still have many similarities. They ingest food and digest it in an internal cavity. They reproduce sexually. They have bodies organized into tissues, which in turn make up organs. They are capable of at least some degree of movement.
Plants and protozoans can share some of these characteristics, but plants can be distinguished from animals by the rigid walls of their cells, while protozoans are single-celled creatures.