According to the NIST Definition of Cloud Computing there are five cloud deployment models:

• Private cloud - OpenStack - on-premise
• Community cloud - limited to a specific community of cloud consumers such as the Fed.gov, CIA, DoD
• Public cloud - Azure, Office 365, AWS, Google Cloud, SalesForce, RackSpace
• Hybrid cloud - combo of public cloud and on-premise private cloud. eg. Azure Stack

• Virtual Private Cloud (VPC) - Known also as a “dedicated cloud” or “hosted cloud”. Results in a self-contained cloud environment hosted and managed by a public cloud provider, and made available to a cloud consumer.
• Inter-Cloud - This model is based on a cloud architecture comprised of two or more inter-connected clouds.

Fair Use Source: http://whatiscloud.com/cloud_deployment_models/other_deployment_models