The skeleton of a Sea Star in indeed an endoskeleton and is inside of an outer covering just like the skeleton of a human.
The skeleton varies with the type of echinoderm but in Sea Stars and brittle stars, the skeleton consists of small ossicles that move with one another forming flexible joints much like our joints of tendons and ligaments. A theory is that the spikes on the sea star are a continuation of the skeleton but even though humans have endoskeletons they do not have any continuation onto the skin other than the outer covering that protects our inner organs.