Hello @C.J. Vieleers

Thank you for reaching out to the Microsoft Q&A platform.

The answer to this question really depends on how you define "cloud". A private cloud is a cloud that is dedicated to one organization and is managed by that organization. This could be a cloud that is hosted on premises or in a third-party data center. It could also be a cloud that combines on-premises infrastructure with cloud-based resources, such as Azure. This type of setup would be considered a hybrid cloud. It is up to the organization to decide how they want to define the term "cloud".

The word "cloud" does not necessarily mean that it is always hosted at a cloud provider like Azure. It refers to the delivery of computing services, including servers, storage, databases, networking, software, analytics, and intelligence, over the Internet ("the cloud") to offer faster innovation, flexible resources, and economies of scale.

Regarding your second question, your vnet with virtual servers that are only available through the ExR (not the internet) from the on-premises network would be considered as a private cloud, as it is exclusive for your company and located on your company's on-premises datacenter. This is not an example of a hybrid cloud, as a hybrid cloud refers to a cloud computing environment that uses a mix of on-premises, private cloud, and third-party, public cloud services with orchestration between the two platforms.

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