There are 3 cloud deployment models.
Public Cloud: The infrastructure is owned by your cloud provider and the server that you are using could be a multi-tenant system.
Private Cloud: The infrastructure is owned by you or your cloud provider gives it to you as a service exclusively.
Hybrid Cloud: When you use public cloud, and private cloud together, it is called Hybrid Cloud. For example, use your own servers for authentication/confidential data while using the public cloud for hosting the company's public website.