Public cloud is “the cloud” in general discussion. As defined by Google: “Public cloud is a type of computing where resources are offered by a third-party provider via the internet and shared by organizations and individuals who want to use or purchase them.”
Public cloud also provides a locally runnable option of public cloud. This way you can benefit from some of the public cloud services and benefits but run them locally in a data center. Examples include: Google Anthos, Azure Arc and AWS Outpost.