Me: "Other than some temperate mollusk eaters and the crown of thorns, the diet of most traditional sea stars is unknown."
You (OP): "But dont most sea stars eat clams. Because I know the ones at the tide pool I go to do?"
Me: "Well, where is the tide pool that you go to? ...the stars in the tide pool are likely the temperate mollusk eaters that I mentioned."
You (OP): "I go to a tide pool that is in Main. But are the Burgundy and marble stars temperate? I'm confused"
My reply: The starfish that you see in a Maine tidepool are from cool temperate waters, and would fall into my generalized category of "temperate mollusk eaters." And, indeed, you state that you have seen them eat "clams."
As far as the "Burgundy and marble stars" in your query -- first, that description doesn't give me much to go on as far as what species (or even genus) of seastar you are referring to; these could be species of Fromia, Linkia, Nardoa or any other genus.
However, I assume your question is about a tropical species available in the trade, as many Fromia sp. are refered to as "marble stars."
To be clear, it was never my intention for you to infer that these seastars may be "temperate mollusk eaters." Rather, these starfish would fit in my generalized category of having unknown diets and thus not fairing well in most of hobbyist's tanks.
First, a caveat: Most reef-keepers know the general rule-of-thumb about traditionally-shaped seastars -- that is, the "bumpy ones" are carnivores of "meaty" foods. Well, collectors, wholesellers, and retailers also know this "rule," and they are aware that seastars labeled "Fromia" and "Linkia" sell better than unidentified seastars. Since many hobbyists wouldn't be able to identify the differences between the various Asteroidea seastars, most imported seastars are labeled as either "Fromia" or "Linkia" and few people recognize if the starfish is misidentified. This only adds to the confusion re: keeping stars in tanks.
According to Dr. Shimek in his Marine Invertebrates book (Pocket Expert), several Fromia sp. found in the trade either have an unknown diet or feed primarily on live sponges. The situation is similar for Linkia, for which the "natural and necessary diet is unknown." Thus he determines that these seastars are inappropriate for most tanks as the star will "die of malnutrition."
As finsurgeon mentioned, I have also read that these stars feed on the "organic film" on live rock, something that simply can't currently be replicated by prepared foods. This organic film may consist of film algae, sponges, encrusting organisms (e.g. bryozoans and forams), small motile invertebrates (e.g. copepods and amphipods), and bacterial films.