Well, doesn't tango have a lot of cliches to live up to! Tango sits apart from the other ballroom dances, and has a very different history. While foxtrot, waltz, quickstep, and Viennese waltz have their roots firmly in European and Anglo-American culture, tango's roots lie in Argentina. The dance has had many incarnations. From its Argentinian origins, it travelled to North America and changed a bit. Following its popularity there, it became a rage in Britain and Europe, most notably in France, where it evolved further. The new version of tango travelled back to North America and developed further still, forming the basis of the version of tango that we teach.
Meanwhile, the dance continued to evolve in a very different direction in its original home of Argentina, and has once again become globally popular as Argentine tango. The two dances are quite different from each other (although their shared history is evident if you're familiar with both styles), and they're both completely different from the earlier dances which are their shared ancestors.
The style of tango we teach is characterised by strong, sharp, dramatic movement. Argentine tango is softer and more romantic, but nonetheless has elements of tension.
Tango music is a genre of its own. Here are some examples, some of which have the fire of ballroom tango, while others have a smoothness more suited to the Argentine style. There are some traditional and some contemporary ones here.