An Azure virtual machine is an instance of a system, this can be a windows or linux VM that the user can admin. You can have access to multiple VMs at the same time along with administrative powers over them.
An Azure Cloud Service (a web role, a worker role, etc.) is a layer above the VM. Azure controls the VM instance that your role runs on (O/S, updates, etc.), while you are just concerned about your application. Cloud service provides a wide range of possible resources that you can access and use at your own convenience.
If a person is working with a virtual machine, Azure VM is the most useful resource. However, if you're developing applications and aren't as concerned over the infrastructure (O/S updates, etc.), then the cloud services provided by azure can be very resourceful.
It entirely depends on the type of work that you are concerned with.
To get to learn more about Azure virtual machines, check this video out
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