Final answer:
The Schengen Zone is the area within the EU that allows passport-free travel across borders, distinct from the Eurozone, which is about the common currency.
Step-by-step explanation:
The area of the European Union (EU) that has agreed to passport-free travel across international borders is known as the Schengen Zone. This zone includes most EU countries as well as a few non-EU countries, allowing for ease of mobility for citizens to travel and work without the need for passport checks within this area. The Schengen Area is separate from other aspects of the EU, such as the Eurozone, which refers to the group of EU countries that have adopted the euro as their common currency.