Different types of clouds in cloud computing include public clouds, private clouds, and hybrid clouds. Public clouds are owned and managed by third-party providers, offering resources over the internet. They are scalable and cost-effective but may lack customization and control. Private clouds, on the other hand, are dedicated to a single organization, providing more control and security. Hybrid clouds combine elements of both, allowing data and applications to be shared between public and private environments, offering a flexible solution to meet different organizational needs.