Maybe you have observed two different states when you turn off a virtual machine in Azure: Stopped and Stopped (Deallocated). The question is whether what state machines continue to be charged.
You can stop the virtual machine by connecting via RDP and off by Windows, in this case it will be with status Stopped in this state it will continue charging and the internal IP and the public will be preserved.
Please note that the IP addresses were kept
It has been the state of the machine is in Stopped (Deallocated) means that you have made a shutdown by Web Management Interface Azure ( SHUTDOWN BUTTON ). In this way the cost of virtual machine will not be charged, but the public and internal IP will be deleted.
Note that the IP addresses were excluded (internal and public), if you do not book a public IP (maximum of 5 per signature), you may notice that you have a web site or application on this machine, the web site / application will be unavailable and when turning it back as a new public IP will be provisioned. You have to do a DNS entry manually if you are accessing by a proper name.
If your virtual machines are in production, already gave to note that you should never turn off the virtual machine for the web interface of Azure.