People get confused and try to reconcile what "cloud" means in the terms public cloud and private cloud. To me they are contranyms. Those are words that are spelled the same but have two entirely different meanings.
For example, the word "fast". It can mean to move rapidly. The runner ran fast. It can also mean to be held tightly. The mast held fast to the ship during the storm. Another example is "clip". He clipped the papers together. He clipped the coupons from the newspaper.
The world cloud is being used in two different ways. In public cloud, the term cloud refers to utility computing which is effectively massively scalable. In private cloud, the term cloud refers to a virtualized computing environment which is not massively scalable.