A cloud deployment model defines where the physical servers are deployed and who manages them.

Public Clouds
Public clouds provide access to computing resources for the general public over the Internet but the resources themselves are owned by the organization selling the cloud services. The public cloud provider allows customers to self-provision resources typically via a web service interface. Customer's rent access to resources as needed on a pay-as-you-go basis. Public clouds offer access to large pools of scalable resources on a temporary basis without the need for capital investment in data center infrastructure.
With public cloud, infrastructure costs are shared across customers, which result in economies of scale. Data control might be an issue depending on a number of factors, including the type and sensitivity of the data as well as the industry and local laws concerning the data.
Private Clouds
Private clouds give users immediate access to computing resources hosted within an organization's infrastructure and the resources are dedicated solely for that organization's use. Users self-provision and scale collections of resources drawn from the private cloud, typically via web service interface, just as with a public cloud. However, because it is deployed within the organization's existing data center—and behind the organization's firewall—a private cloud is subject to the organization's physical, electronic, and procedural security measures and thus offers a higher degree of security over sensitive code and data.
With private cloud, the performance of physical hardware can be controlled and maintained by the organization, and can thus markedly improve data center efficiency while reducing operational expense.
Hybrid Clouds
Hybrid clouds combine one or more public clouds and one or more private clouds by technology that enables data and application migration between them. Hybrid clouds typically use a shared API to enable hybrid operation.
With hybrid cloud, organizations can utilize the cost benefits of a public cloud and when needed, protect confidential data in a private cloud.
