James Serra argues that virtualization does not by itself make for a private cloud:
Since virtualization only solves #3, a lot more should be done to create a private cloud. Also, a cloud should also support Platform-as-a-service (PaaS) to allow for application innovation. Fortunately there are products to add the other characteristics to give you a private cloud, such as Microsoft’s Azure Stack. And of course you can always use a public cloud.
Read James’s post to get the full listing of what makes for a “cloud” offering.