Turns out the answer is both homology and convergence.
Those huge and fascinating starfish and octopus ‘arms’ are oversize ‘lips’ surrounding a central mouth. This trait is also found, much reduced, on the last common ancestors of both taxa, nematodes and lanclets (Figs. 1-3). On the other hand, the ‘suckers’ that line starfish and octopus ‘arms’ are convergent. Their last common ancestors do not have suckers, but one might have homologous precursor structures (Figs. 4, 5). Or not.
The starfish is a radial animal
with a mouth at the center of five radiating arms that help it grasp prey, travel across the sea floor and draw food to the mouth.
The octopus is a radial animal
with a mouth at the center of eight radiating arms that help it grasp prey, travel across the sea floor and draw food to the mouth.
had a bilateral, worm-like last common ancestor that evolved in two different directions: echinoderm and mollusc. Then some members of both clades expanded their radial mouth parts, reducing and deleting other body parts.
Earlier we looked at the last common ancestor
of molluscs and echinoderms, enoplid nematodes (Fig. 3, genus Enoplus). We also looked at the most primitive chordates, hagfish (Fig. 3, genus Myxine) and the most primitive molluscs, garden slugs (crawling bilateral molluscs without shells, Fig. 3). These taxa all share the same worm-like, bilateral body plan. All three depend on external secretions of mucous either to slide upon (nematodes and mollucs) or to eject in vast quantities when disturbed (hagfish). Neither the starfish, nor the octopus depend on external mucous secretions. The ‘ink’ sac of cephalopods creates highly concentrated melanin, not mucous.
In the video below,
octopus expert Danna Staaf begins octopus evolution with a snail-like cephalopod with a small, chambered, conical shell and tiny ‘arms’. That’s the traditional story. And it’s probably true. But what came before such shelled molluscs? Answer: Bilateral worm-like molluscs without shells (Fig. 3). Slugs tie snails to mussels and cephalopods.
Both starfish and octopus ‘arms’ are large, fleshy, mobile projections
at the circumference of the oral cavity. Such structures are first found in nematodes, like Enoplus (Fig. 3), and basal chordates, like hagfish (Fig. 3) and lancelets (Figs. 4, 5) where they are soft, tiny and delicate at their genesis. On lancelets, these external sand filters are called oral or buccal cirri. In starfish and cephalopods, these grow to enormous sizes as they take on more duties. At the same time, the rest of the body shrinks, more so in starfish than in octopuses, which develop eyes, brains, siphons and other body parts not found in starfish. Even so, in lancelets, starfish, slugs and octopuses, the oral cavity remains ventral.
Starfish and octopus arms are not simple structures.
Both sets of arms are complicated ventrally with flexible suckers. Are these homologous? Not exactly. A close view of buccal cirri in lancelets reveals pointed lateral projections that act like sand screens. At present it appears that suckers developed convergently in starfish and octopuses probably de novo between those tiny projections.
These are not the only related taxa to expand the mouth
(= oral cavity) and reduce the rest of the body. Tunicates and crinoids also do so, but in different ways, like expanding the atrium. We looked at their strange body plans earlier here.