Elkhorn coral is a wide term, I see it most oftenly applied to a form of Montipora.
While most divers also recognize Elkhorn as A. palmata, it's not that common in the hobby. And frankly, even if it weren't protected, it's the sort of massive coral that IMO isn't a good fit with an aquarium - not colorful, would take years to grow + then would require most of the tank.
As for the SPS/LPS classification - that's a hobby thing. IMO, finding about it's wild habitat would tell you more about how to care for it.
Personally IMO, if it's a protected species, I don't like it associated with this hobby.