My friend Dave Vellante at Wikibon Project, a new crowdsourced analyst firm, put together a nice image on the private vs public cloud.
Public vs Private Cloud Computing
There are as many definitions of cloud as there are technology bloggers. However, the major theme is that a Public Cloud provides IT resources that are provisioned remotely from the consumer and operated by a third party.
In a Private Cloud, the infrastructure policies are governed by a single organization where workloads and data can be moved to and from internal and external data centers. Private Clouds provide an organization a single point of control for security, manageability, privacy, audit, compliance and governance.
However the business case for engaging in a public or private cloud strategy involves several factors, the most important being business revenue and/or budget.