"Is this a case of Americans inventing a term no one else uses?"

Right now in the American medical field, it seems that the trend is to move away from calling diseases after people. What has been known commonly as Lou Gehrig's Disease is now being referred to by its more descriptive name, Amyotrophic Lateral Sclerosis, with "Lou Gehrig's Disease" in parentheses. Alzheimer's hasn't undergone this transition yet, but I have no doubt that it will!

As for Paget's Disease, this name is confusing because it is the common name of TWO different diseases: (a) a metabolic disease of the bone; and (b) inflammatory breast cancer. In this case, it makes sense to try to "phase out" the use of the term "Paget's Disease" for inflammatory breast cancer.