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The Definition of a virtual appliance is a prebuilt, preconfigured and preinstalled. So any VM which has already been created, Configured and installed can be called as a Virtual Appliance. Now OVF stands for Open Virtualization Format. Its just a format or extension and the main purpose of ovf format is that it compresses the VM (Like a RAR or ZIP) so as to be easily transported. So the main purpose of OVF is for Transportation. In the VA Marketplace, thats the reason why the appliances are in OVF format so that they can be easily transported to any virtual environment.
You may also create VMs, configure them and install everything then export it in a OVF format and you can call it as a Virtual appliance. Means doesn't matter, whether they are from studio, server or Esxi. Hope this clears your query.
Yes, Export the vm to an OVF template is an appliance and then you can import it any time. Virtual Appliance is a preconfigured machine.