well, smooth jazz isn't jazz. its a mockery of jazz. don't listen to it.
other than that, there are many sub genres of jazz that are all quite different.
Dixieland/New Orleans jazz is the oldest form of jazz and is characterized by group improvisation by usually a cornet, trombone and clarinet, with banjo, drums and tuba as the rhythm section. early Louis Armstrong is a good example
big band jazz is characterized by more solo improvisation rather than group improv. as in New Orleans jazz and the ensemble is much larger. usually 5 trumpets, 5 trombones, 5 saxes, piano, bass, drumset, guitar. Count Basie's band is a good example
bebop is basically a reaction to big band jazz in the 30s/40s. the ensemble drops to piano/guitar, bass, drumset, and two to three horns. the music is generally fast and there is an emphasis on the skill of the soloist. Charlie Parker is the essence of bebop.
Cool jazz is sort of a reaction to bebop, the music is medium to slow and is far more relaxed than bebop, hence the term "cool" jazz. Miles Davis's "Kind of Blue" is a good example of this style.
Hard bop is a style that comes from bebop that is very similar to bebop. the chord progressions and melodies in hard bop tend to be a little more traditional or simpler than that of bebop, though the intensity level remains fairly high.
free/avant garde jazz is a style that is generally completely improvised. there is no real way to describe free jazz because it varies so much between different artists. Ornette Colman, Sam Rivers, Ken Vandermark, and Cecil Taylor all play free or avant garde jazz.
Latin jazz is a fusion of jazz and afro-carribean and central and south american musics. mainly brazilian, cuban, and puerto rican.
Eddie Palmieri and Brian Lynch's album "simpatico" is a good example. also "Getz/Gilberto" is a good example of brazilian jazz.
jazz fusion is generally fusion of jazz and rock/funk but can be anything really. Return to Forever, The Mahavishnu Orchestra, and Weather Report are some examples of fusion
Modern Jazz is also fairly hard to describe, it is generally a far more complex version of both bebop and cool jazz with a full range of possible tempos and intensity levels. big bands and small groups are used. Chris Potter, Freddy Hubbard, Roy Hargrove, Will Vincent, Bill Frizell, Kurt Rosenwinkle, and Wayne Shorter's newest music are all good examples.