The EU's Freedom of Movement is a remarkable achievement. It's far from world wide and doesn't even aim for that, but it does allow you to move freely in ~30 sovereign countries. (Shame some 70 million of us just lost it)
Even for you it means that if you get a Schengen visa (ie a visa for a country in the Schengen zone) that you may travel freely around the Schengen zone with that visa for 90 days