I don't know why W1 is considered tool steel, if it's a carbon steel that has the same amount of carbon as 1080 steel. ISO calls it C80U, and 1080 C80, so they are very similar. So what makes C80U so special?
I doubt it is more than a name ,or call it 110 Class tool steel in US. I always wondered about the P 1 to 5 "tool steels" because they are ordinary low carbon low alloy steels. One specific difference can be price; Something priced as a "tool steel" may have a different price from "AISI 1080 hot rolled ". I have not seen this in tool steels but I have seen it in pipe. When pricing 13 Cr pipe, two mills had substantially different prices ( same pipe). We found one mill called it alloy steel . The other mill called it "stainless steel" and added a much higher overhead to the basic cost of the pipe.