I think you're belabouring your question; the definitions have been given clearly and correctly -- you just seem to want some other answer..... sorry, but I think you just need to read the explanations given once again. International means between a number of countries, all of which use the same language.
German, for example, is used in Germany, Switzerland, Austria and Luxemburg.
Sorry for any incovenience. Thanks.
Keep my fingers crossed for you.