I am not a lawyer and every state has its own laws governing this. What I can tell you the definition of "training" does not confer expertise on any injector, nurse practitioner or physician. There are folks who are "trained" that spend an hour with a nonphysician sales rep who shows them how to inject Botox or Juvederm in a crash course. The company obviously wants to put their products in the hands of as many injectors as possible. Then you have physicians like dermatologists and plastic surgeons who "train" for several years and learn the anatomy, the nerves, the arteries, the veins, the muscles of the face in detail and are supervised by board certified physicians that teach them how to inject and they perfect their skills over years.
The two are not equivalent.