Private cloud refers to a model of cloud computing where IT services are provisioned over private IT infrastructure for the dedicated use of a single organization. A private cloud is usually managed via internal resources.
The terms private cloud and virtual private cloud (VPC) are often used interchangeably. Technically speaking, a VPC is a private cloud using a third-party cloud provider's infrastructure, while a private cloud is implemented over internal infrastructure.
Private clouds may also be referred to as enterprise clouds.
The main difference between private and on premise infra is the fact that private still has some managements or monitoring part taken care by the vendor