It’s a ‘shell’ because it protects you from the elements. These days, soft shells and hard shells perform the same function (as noted, keeping wind, snow, and water out) the difference being the soft shells are meant for more active scenarios (hiking, climbing, skiing, etc.) while hard shells are meant for periods of inactivity or severe weather. This is because soft shells are more breathable, but hard shells do a better job of keeping you dry. You also have the option of putting your hard shell over your soft shell in a pinch (a sudden wind storm or blizzard that the soft shell can’t handle and when it is not practical to remove the soft shell first). Increasingly, the line between them is becoming blurred, at least in most situations. I use a ‘hybrid’ that sits somewhere between and should suffice unless you are in a blizzard in the arctic or the Himalayas. Not that I do much hiking or mountaineering these days, but it works fine when out in the rain too.
They do not keep you warm, though. That’s what the insulation layer is for, so don’t go buying one of those if you are looking for an all-purpose winter coat or something. The layer beneath the insulation layer is the base layer, which wicks sweat away from your body. This is so you do not freeze to death from your own sweat, which happens more than you’d think!