Terminology
The word "international" in an airport's name usually means that it is an airport of entry, but many airports of entry do not use it. Airports of entry can range from large urban airports with heavy scheduled passenger service, like John F. Kennedy International Airport, to small rural airports serving general aviation exclusively. Often, smaller airports of entry are located near an existing port of entry such as a bridge or seaport.
On the other hand however, some "former" airports of entry chose to leave their name with the word "international" in it, even though they no longer serve international flights. One example is Osaka International Airport, or Itami Airport as locals call it. Even when Itami had ended all international services and became a purely domestic airport after the opening of Kansai International Airport in 1994, it kept its original name of "Osaka International Airport". Many airports in the nearby region have the same situation, like Taipei Songshan Airport. Songshan retained its official Chinese name, Taipei International Airport, after Chiang Kai-shek International Airport (now Taiwan Taoyuan International Airport) opened.
For the European Union, flights between countries in the Schengen area are considered domestic regarding passport and immigration check. Several international airports have only intra Schengen-flights. Several of these have occasional charter flights to foreign countries.
Read more about this topic: Airport Of Entry