Sclerotia are compact, hardened masses of fungal mycelium that store nutrients and help the fungus survive tough conditions. When conditions improve, a sclerotium can produce above-ground fruiting bodies known as mushrooms.
Magic truffles are simply the sclerotia of certain psilocybin-producing fungi. They are part of the same organism as psilocybin mushrooms but are not the mushroom itself.
In mycology they are not considered mushrooms because they are not the fruiting body. Legal status varies by country; in the Netherlands, fresh sclerotia have been sold while psilocybin mushrooms have been banned since 2008. Please check up-to-date local regulations.
You may see truffles sold under names like Mexicana, Tampanensis, or Atlantis; for a concrete example, see Magic Truffles Triptane. Hope this clarifies the distinction.