As I understand it, legally even the simple stamp in a passport counts as a "visa", even when one does not have to apply (and pay) for a visa ahead of time. He

As I understand it, legally even the simple stamp in a passport counts as a "visa", even when one does not have to apply (and pay) for a visa ahead of time. Hence all of these various "visa waiver" schemes have been mis-named, they're just simpler/cheaper/easier visa schemes.