History don't matter the category of bikes. Doesn't matter if dirt bikes came from BMX. It isn't a trial bike and it isn't for same stuff. period.
BMX
chav
Trial bike (notice the frame)
Used to pass different "tracks" where you have to jump on objects and do balancing with one wheel for example etc etc
works the same way as motored trial bikes.
http://www.pinkbike.com/photo/ ... tegory=7&date=2011-02
Dirt bike / street
For tricks you do by going from jumps that throws you in the air high.
(look at my bike for example)
DH
Hi speed going on a downhill trail with jumps that throws you miles away. professionally time attacking or whatever it's called.
Freeride
Name tells everything. Most likely to have full suspension bikes with more travel than normal bikes. Bikes go same category than DH but there can also be some hardtrails. You don't race in freeride. Just jump/go fast..
4X bike
Racing on wide dirt track.