Often all-season refers to all seasons except the winter, while all-weather includes winter weather too. This is a bit confusing. Both are a compromise but can be used in different conditions. If you are not looking for the highest performance and you don’t have harsh winters, then both all weather tires and all-season tires are worth considering.
It is wise to check is if they are approved for winter conditions, as some are and some are not. If they are approved you have a good tire for all-year use. If they are not approved for winter use, you will still need a winter tire when winter weather arrives.