The terms "private cloud" and "virtualized data center" are a good example of the general difference between cloud computing and virtualization. Although cloud computing and virtualization offer some similar benefits, they are two fundamentally different IT philosophies and setups.
Private cloud is a type of cloud computing where the cloud vendor provides a special infrastructure for a single client. With public cloud services, vendors using multitenant strategies — the data and resources of one client are handled the same way, and in the same containers, as the data and resources of another client. They are put into the same infrastructure, which creates some security questions. With private cloud, the vendor takes the company data and sends it to a remote vendor location where it is completely separate from any other client data.