Storm drains and sewers are words often used interchangeably, but they are not the same thing. A storm drain usually is constructed as part of a curb to catch excess water runoff from roads to prevent flooding. The storm drain is part of a drainage system that carries that water, untreated, to a nearby source of water.
A sewer, on the other hand, carries sewage from homes and businesses that comes from kitchens, bathrooms, or washing machines. Some water in the sewage system might also come from rain that drains through manhole covers. The sewage carried through a sewer system does get treated at a treatment facility to limit water pollution as much as possible.