Not sure what kinds of differences you are looking for, but they are different species. Atlantic salmon are members of the species Salmo salar. Pacific salmon in the US are made of 5 different species, all in the genus Onchorhynchus. These are the Chinook (O. tshawytscha), chum (O. keta), coho (O. kisutch), pink (O. gorbuscha), and sockeye salmon (O. nerka). Steelhead (O. mykiss) are actually not a salmon, but an ocean running type of rainbow trout. All of these are members of the family Salmonidae.
Also, most Atlantic salmon are farm raised today, whereas most Pacific salmon are wild caught.
** Also a key difference is that the Pacific salmon the "true" salmon die after spawning. The Atlantic salmon are able to spawn several times during their life.