This handy Venn diagram illustrates the relationship between the Council of Europe, the European Union, Shengen, the Eurozone, the European Economic Area, and the European Trade Association. I had to memorise all this stuff for my 'Life in the UK' test when I got my permanent residency permit, and it was actually pretty interesting, especially as compared to some of the other material.
All will be aware of the 'Europe' that is a less than homogenous conglomerate of nation states, with an unwieldy Brussels bureaucracy at its centre. This European Union, which consists of 27 member states, is merely the most visible of several European unions, all committed to different versions of the same goal: European integration.
The EU is formally committed to strive for 'ever closer union' but its members still disagree on how much more than a free trade zone it wants to be. This continuing struggle for the soul of the EU (if that doesn't sound like too much of an oxymoron) is epitomised by the smaller, green circle contained within the blue EU one. These are the countries of the Eurozone, 17 at present, who've jumped in at the deep end of the sovereignty pool by discarding their own currencies in favour of a single one.