A public cloud system is built the same way as a private cloud.
A virtualization layer is added to the resources, and then they are allotted into shared pools and embedded with a layer of administrative control. Next comes the code to automate the repetitive processes.
Imagine going bowling and strapping on a shoe from the premises. Many people would wear the same shoe. This is roughly how the public cloud model works. On the other hand, a private cloud is you renting a shoe specifically for your use. No one else would be allowed to wear it.
The public cloud differs from a private cloud in the underlying fact that multiple users can access a public cloud. In contrast, a private cloud is specific to a particular organization. But the data of each user is hidden from the others.
An organization that decides to adopt a public cloud service can reap many benefits.