As someone who had the (mis)fortune of being raised in the Midwest - storm cellars are designed for short term protection - water, canned food, blankets, flashlights. No power since chances are there wouldn't be electricity after a tornado. Since there isn't a lot of ventilation, no gas fired generator or kerosene heater. (Think of a very small basement with no windows.)
The storms a storm shelter is designed for mostly happen in late summer and autumn.
