There is a big difference.
All season tires work well in three seasons, but they really don’t work very well in that fourth season of winter. Typically, all season tires perform fairly well in the rain.
All weather tires are designed to work well in winter, though they do not work as well as dedicated snow/winter tires.
Nokian makes a couple of all weather tires that do exactly that. They outperform all seasons in the winter, while still doing reasonably well through spring, summer and fall.
So if the OP thinks they’re going to encounter snow, they should seriously look at all weather tires, or, go for all season tires, and a separate set of dedicated winter tires.
If they’re just driving around the Pacific Northwest and encounter a lot of rain, and don’t go into the mountains, or drive in much snow, then all season tires would be a good choice