Hybrid cloud, as the name suggests; it is composed of both public and private clouds. Therefore a hybrid has multiple service providers. For instance, a company might want to implement SaaS application throughout; therefore the required security will be provided by the firewall (private cloud) and the additional security will be provided by VPN (public cloud)
On the other hand, a community cloud service is used by different companies together when they are ready to share the benefits of the cloud. As the cloud provides benefits of both privacy and security, companies having the same requirements often agree on sharing the same.
