Differences:
1. The legend is different.
2. some pokemon are different. (obvious)
3. the city with the 8th gym differs with each version.
4. the 8th gym leader is different with each version.
5. pokemon white has a exclusive area named white forest. you can catch different kinds of pokemon here.
6. pokemon black has a exclusive area named black city. you can buy many different kinds of items here.
now that thats out of the way onto the story which has all new pokemon
but no old 
. the old pokemon appear later.
first steps:
You start the game inside your house. your soon-to-be rivals are there (yes there are 2 rivals now)
. you find a package in your character's room which contains 3 pokemon. after you choose your starter your rivals choose their starter. Now the fun part comes. you must battle your rivals! after winning or losing you must go to the pokemon lab to receive your pokedex.
Route 1:
you learn to catch pokemon here. I caught some pokemon and raised them before moving on.
Accumula Town:
Learn about the pokemon center/mart. Afterwards a group named Team Plasma protests in the streets. a trainer named N challenges you to a battle.
Route 2:
Continue to the next city while battling trainers. One of your rivals battle you here.
Striaton City/Dreamyard:
After arriving heal at the pokemon center. head to the trainer school to battle one of your rivals. Before heading to the gym I HIGHLY RECOMMEND going to the Dreamyard to get the free monkey pokemon. this monkey (type depends on your starter.) can beat the gym leaders monkey (type depends on your starter) no problem. After beating the gym leader heal and head back to the dream yard and battle team plasma.
*wheeze* I am going to stop here for now. Overall i give two thumbs up to this games developers. if you have a ds GET THIS GAME! It will brighten up your day everyday.
