There are three subgenres of tango music: tango, vals, and milonga. Here are several examples.
Tango music tends to follow the habanera rhythm.
Vals is similar to but different from Viennese Waltz, and tends to be both the slowest and the most romantic. This is where the European influence on tango becomes obvious.
Milongas tend to be very fast and are considered the most difficult to master.
There is also alternativo music, when people dance tango to songs outside of the usual three genres.
Some milongas specify outright if their playlist will be alternative.
For non-Spanish speakers, Jake has translated the lyrics to many major songs over the years in his Tango Lyrics Index.