The maxixe was a lower-class dance that caused outrage in upper and middle class society in late 19th century Brazil. Not only did partners hold each other by the buttocks, but – horror of horrors – white women danced with black partners. Nonetheless, the music became very popular in all levels of society.
But you couldn’t, as a respectable lady, go into your local music shop and ask for the sheet music of the latest maxixe, so many composers (falsely) titled their music Tango or Tango Brasileira.
Musically, the maxixe was a fusion of the European polka with Afro-Brazilian rhythms such as the habañera rhythm found in tango or milonga.
As I already mentioned in my Tico-Tico post, we often call things rumbas which are more rightly choro, which in turn comprises the maxixe which is a Brazilian version of the polka. And as you see in this post, that dance was sometimes euphemistically called a tango.
Perhaps you can see now why I won’t be drawn into the ‘what’s the difference between a tango and a habañera’ debate, because the question is founded on false dichotomy in the first place!
As many times before, my source for this stuff is Choro: a social history of a Brazilian popular music by Livingston-Isenhour & Garcia, relevant sections below if you’re in a browser that can view embedded Google books.