The other might be (but I cannot promise you even a chance of dredging that, unless you were off the coast of Portugal, or the windward side of some of the West India Islands) a live Crinoid; an exquisite starfish, with long and branching arms, but rooted in the mud by a long stalk, and

One day they saw a pretty starfish.

On pulling up a useless Starfish instead of a real fish, the fisherman tears the offender in half and throws the halves back into the waves.