All-season tires are basically summer tires; they are tires that have excellent properties at temperatures that are above freezing. They can handle dry and wet surfaces and perform well even in heavy rain.
All-weather tires can be used in all weather conditions, so you can forget the forecast. They can handle the full temperature spectrum, from warm summer weather to cold winter temperatures. When you have cold weather they act as winter tires and can create mechanical traction through the tread pattern. These tires can therefore be used all year round.
In areas where winter tires are required, you can use winter-approved all-weather tires. You can also use dedicated winter tires, which should only be used during the winter season.