"Both are a small groups of weird little worms that are usually found in deeper water and burrow in the mud," Te Papa's collection manager Andrew Stewart says.
However, a Department of Conservation scientist says they are Urechis novaezelandiae otherwise known as Spoon Worms. Originally, they were thought to be Hagfish.
The worm secretes a vast amount of sticky mucus, which it smears over its burrow walls and stretches out to make a net.
When the net is loaded with trapped food particles the worm moves up its burrow and swallows the net and its contents.
Otherwise known as the "fat inn-keeper", they're used in Korea for food, often eaten raw with salt or stir fried with vegetables.
They're also used for bait when fishing.
There are only about 150-165 known species of spoon worm, but they can be quite common in some marine ecosystems.
Looking like a half cooked sausage with teeth, whatever the creatures are, they've certainly sparked confusion.
Acting manager for the National Aquarium, Kerry Hewitt, said the worms were Echinoderms, which is the common name given to any member of the phylum Echinodermata of marine animals.
"In the mass of shingle moving on and off the beach in the tides, they get knocked about and subsequently die. Some were also found on Marine Parade this week."
At one end of its body, the worm has a scoop-shaped proboscis or an "extensible tubular sucking organ."
The proboscis can extend up to 10 times its retracted length in some species.
Whatever the creatures are, here's hoping the sea doesn't wash anymore upon to Hawke's Bay shores anytime soon.