Summer tires use a compound that stays flexible in warm weather and a tread designed to clear water. They give the best dry and wet grip above roughly 7 C, and they harden and lose grip below it.
Winter tires use a softer compound plus thousands of small slits called sipes that bite into snow and ice. They are not only for deep snow - the advantage starts as soon as temperatures drop below about 7 C, on cold dry roads too.
All-season tires split the difference. In a mild climate they are a sensible single set. Where winters are properly cold or snowy, a dedicated winter set will out-perform them by a wide margin.
If you run two sets, ask about seasonal storage so you are not finding space for eight wheels at home.