Cloud deployment models include public, private, hybrid and community cloud models.
When a cloud service is available to everyone over the internet it is called a public cloud.
A private cloud is available only to a single client or a limited number of users and can be setup on-premises within the company firewall or off-premises. A Virtual Private Cloud (VPC) is a private cloud built using shared computing resources allocated within a public cloud environment. Managed Private Cloud refers to a principle where a private cloud serving a single client organization (tenant), and managed by a third-party. This is in contrast to multi-tenancy where multiple client organizations are on a single server.
A Hybrid Cloud combines the services of multiple clouds such as public and private clouds. Secured applications and data may be shared on a private cloud whereas shared applications and data may be stored on public clouds for cost effectiveness.
There may be also Community Cloud deployment models where services may be shared by organizations that have the same policy and compliance considerations.