I am trying to figure out the difference between a reducing die, and a Swedish die? I also am looking for something that will do US quarters and US half dollars, clads to start with, but I can’t seem to find a tool that can do both of these. Can you advise?

There are actually 3 different types of dies. Folding/reducing 17 degree dies, reducing/fat tire 25 degree dies and Swedish dies at 5 degree.
The most important die is the 17 degree folding reducing. This is the primary die for folding the coin to a cone then reducing the cone into a ring. You’ll need a steel starter cone and universal plastic folding cones to do this. The 25 degree die is optional to hel;p get a few sizes smaller and make a more rounded or”fat tire” look. the Swedish dies are also optional but give you more options in sizes as you can take rings down to a very small size, making straight walled rings and they also help to remove any wobbles.
The .9 x 1.0 @ 17 degree will fold and reduce U.S. quarters and similar sized coin. U.S. quarters are just under 1.0 inches, therefore they work in that die. U.S half dollars are 1.2 inches in diameter, so the 1.1 x 1.2 17 degree die is used to fold and reduce thoughts. As the ring gets smaller, you’ll need smaller dies. As you stretch it out, you’ll need bigger dies to finish it off.