Although I have no intention to plot the perfect map of the Jazz world, it is not bad to have a rough idea about the world you are traveling in.
Different sources paint different maps, but this is what I have as my probably generally acceptable overview.
It all starts around the start of the 20th century, not only but mostly in New Orleans. The early heroes being Louis Armstrong, Sidney Bechet and Jelly Roll Morton. Then Jazz moves on to Chicago and New York and has probably its peak in popularity with the Bigband Swing. Count Basie, Benny Goodman, Fletcher Henderson and obviously Duke Ellington as important names.
Starting in the 30ies, Charlie Parker and Dizzy Gillespie move the Jazz out of the dance halls and clubs and make it more a “musician’s music”, creating the Bebob. At the end of the 1940ies as a response to the nervous Bebop, the Cool Jazz becomes popular and with it Miles Davis. To counter the Cool Jazz then Hardbop is created.
Later it gets more difficult with the nice mapping, with the Free Jazz 1960/70 things get a bit out of control. John Coltrane and Ornette Coleman lead the Jazz into new territories. Latin Jazz combines many influences and has many exponents (Chick Corea, Tito Puente, Stan Gets, etc).
And where are we today? Wynton Marsalis combines Jazz and Classical Music, there is Acid Jazz and Smooth Jazz. It seems that no style really dominates and the same musicians play various types of Jazz, sometimes with different formations, sometimes even in the same performance.