
The Kraken is not a creature of Greek mythology. It comes from Scandinavian sea folklore, and no ancient Greek source mentions it. People searching for the "Kraken in Greek mythology" usually mean the sea monster of Clash of the Titans, where the Kraken stands in for the Greek monster Cetus (Ketos), the beast that Poseidon sent against Andromeda.
Scandinavian sailors and fishermen told of enormous sea creatures long before the name Kraken was written down. Medieval Norse tales such as Orvar-Odd's saga describe huge sea beasts, the hafgufa and the lyngbakr, but they do not call them Krakens. The name itself, from Norwegian krake, appears in the 18th century. In his Natural History of Norway (1752-53), the Bishop of Bergen Erik Pontoppidan described the Kraken as a creature as big as a floating island that could drag ships down and stir a whirlpool when it sank. Later writers turned it into a giant squid or octopus, and sightings of real giant squid probably helped the legend along.
The link comes from film. In Clash of the Titans (1981) the hero Perseus must face a sea monster called the Kraken to save Princess Andromeda, and the line "Release the Kraken!" became famous. The 2010 remake repeated both the monster and the line. The Greek story the films retell never named a Kraken at all, and that is why the creature is often mistaken for a Greek one.
In the Greek myth, told by Apollodorus (2.4.3) and in Ovid's Metamorphoses (book 4), Queen Cassiopeia boasted that she, or her daughter Andromeda, was more beautiful than the Nereids. Poseidon was angered and sent a flood and a sea monster, Cetus, to ravage the coast of Aethiopia. An oracle told King Cepheus that the only remedy was to give up his daughter, so Andromeda was chained to a rock by the sea. Perseus, flying home from killing Medusa, saw her, agreed to rescue her in return for her hand, and killed the monster. In Ovid he strikes it with his sword; in later versions he turns it to stone with Medusa's head, the version the films follow. Cetus was placed among the stars as a constellation.
The Greek word ketos meant any large sea monster or whale, and gave us the word "cetacean". The sea goddess Keto, whose name is the feminine form of ketos, is the mother of several Greek monsters, though no ancient source names Cetus among her children.
The Kraken is a tentacled sea monster that wrecks ships. Cetus is a punishment sent by a god against a royal house, defeated by a hero. Greek mythology also has sea monsters that did attack sailors, such as Scylla and Charybdis, whom Odysseus faced, but none is a Kraken. See also the Sea Monsters of Greek mythology and the other Monsters of the Greek world.