No SS, if it were acting like a serpent star it would neither be in the sand nor the rocks, it would be wrapped around a branching gorgonian or branching coral like the proverbial serpent in the Garden of Eden :wink:
Really, the aquarium trade does not use the common names the same way that biologists do. And biologists don't always use standardized common names amongst themselves either.
All echinoderms that we call "starfish" are of one class known as Stelleroidea. They are then divided into 2 subclasses, Asteroidea (known as sea stars) and Ophiuroidea (known as brittle stars, serpent stars and basket stars). There is also an animal we call feather star or crinoid, but this is not like the Stelleroids and is its own Class and is not technically a "starfish".
It seems that some species of the subclass Ophiuroidea habitually wrap themselves around branching things and have a snake-like appearance - these may commonly be called "serpent stars". Other species of this subclass are also snake-like in appearance but don't wrap around branches - these may be called "brittle stars". Other species of this subclass have very finely and many-branched arms (giving the appearance of having hundreds of arms) - these may be called "basket stars".
Now, it can get a little confusing because what I just described as serpent and brittle stars can collectively be called brittle stars because their bodies are literally brittle. The basket stars are generally always called basket stars; but in a sense they are brittle stars too because their bodies are also brittle.
One reference I have calls all the Ophiuroids "brittle stars", and divides them into serpent stars and basket stars.