At a very high level, you are correct to think of a cloud provider as just another datacentre with Hyper-V hosts bundled together to provide virtual machines resources to other companies.
There are, of course, a lot of other considerations that comes into play once you start looking at the details, such as segregation (how to ensure that a VM belonging to company A cannot communicate with the VM belonging to Company B, while running the same host), security (make sure that no unauthorised access can get through), storage, etc.
The above is referred to as "Infrastructure as a service" or IaaS in the cloud industry, and is effectively delivering the platform to other companies to run their virtual machines, so that those companies do not need to worry about hardware maintenance, datacentre management, hypervisor updates, etc.
In addition, two other cloud categories are available today:
- Platform as a Service or "PaaS"
With this type of cloud service, the delivered workloads runs at a higher level than just VMs. For example, you can get a SQL database as a resource through this offering. This means that you no longer have to take care of virtual machines the SQL database runs on. It's yet another level of abstraction from the hardware up to the application
- Software as a Service or "SaaS"
Yet another level above PaaS, where everything (including the application) is maintained for you and you consume only the service itself. A great example of SaaS is email in the cloud (such as outlook.com or gmail) where you only consume the emailing services without having to maintain the hardware or software that comes with it.
There are a lot more details that can be given, which would be too long to write within this forum. For more details, I would suggest to take a look at the Azure Fundamentals site:
https://learn.microsoft.com/en-au/learn/paths/azure-fundamentals/
This will give you a great overview (in a modular, led learning way) of the basic of cloud computing, as well as the basics of Azure IaaS principles (VM, Storage, Networking), Security, and more...
Cheers,
Stephane
(Please don't forget to accept helpful replies as answer)