The European Union is the biggest political and economic union on the continent, currently with 27 member states, 24 languages, and 3 different scripts. Of these countries, 20 are also part of the monetary union, the Eurozone, or the Euro area. Montenegro and Kosovo despite not being part of the EU, and thus Eurozone, use Euro. A bit more complicated is the Schengen Area. There are 26 states, which might sound like all EU countries but one, however, it is not: Most EU countries are part of the Schengen Area (21, all except four: Bulgaria, Cyprus, Ireland, and Romania). The other four are no-EU countries belonging to the so-called EFTA (European Free Trade Association), a regional trade organization and free trade area, consisting of Iceland, Liechtenstein, Norway, and Switzerland.
The group of European microstates (Andorra, Monaco, San Marino, and the Vatican City) are not part of the EU nor NATO, however, all of them use the Euro thanks to a formal agreement. Moreover, three of them (all but Andorra) have open borders with Schengen, without being part of it.
Finally, NATO (North Atlantic Treaty Organization) is a military alliance between 30 member states, 2 North American and 28 European. Again it is not as simple as it looks: 21 EU countries are part of NATO and 6 are not: Austria, Cyprus, Finland, Ireland, Malta, and Sweden maintain a position of neutrality from the Cold War. The rest of the European NATO countries are non-EU states: Albania, Iceland, Montenegro, North Macedonia, Norway, Turkey, and the United Kingdom.