Cellar spiders are the long-legged, pale ones hanging upside down in loose, messy webs in basement corners; they shake the web when disturbed. Common house spiders are small, tan to gray, with a round abdomen, and build the cobwebs in room corners and around windows. Wolf spiders are bigger, brown and hairy, with no web; they hunt on the ground and are the ones that run across a basement floor or garage. Jumping spiders are small and compact, often black with white marks, move in short hops, and are out in daylight on window sills and walls.
Two things that are not house spiders: daddy longlegs, which have one round body segment and are harvestmen, not spiders; and house centipedes, which have many long legs, move fast, and are a moisture sign, not a spider problem. Bites from the spiders that live in Long Island homes are rare and almost never serious.