Like many things in crochet, you’ll find multiple ways to name the sizing of hooks. Note that some of the sizes don’t have corresponding sizes in all the others.
You’ll also find size differences among manufacturers. When in doubt, either use millimeters (it’s an actual measurement) or just plain measure your hook.
These things are just part of the “fun”. Just go with it and know that they exist.
I give you two of the most popular below.
Note that this is important enough that we suggest that you print it for reference.
This is just a sampling of what’s in our Crochet 101 PDF!