Briareus said to be the same as Aegaeon
Names
The three Hundred-Handers were named Cottus, Briareus and Gyges. Cottus (Κόττος) is a common Thracian name, and is perhaps related to the name of the Thracian goddess Kotys. The name Briareus (Βριάρεως) was probably formed from the Greek βριαρός meaning "strong". Hesiod's Theogony also calls him "Obriareus". The name Gyges is possibly related to the mythical Attic king Ogyges (Ὠγύγης). "Gyes", rather than Gyges, is found in some texts.Homer's Iliad gives Briareus a second name, saying that Briareus is the name the gods call him, while Aegaeon (Αἰγαίων) is the name that men call him. The root αἰγ- is found in words associated with the sea: αἰγιαλός "shore", αἰγες and αἰγάδες "waves". The name suggests a connection with the Aegean Sea. Poseidon was sometimes called Aegaeon or Aegaeus (Αἰγαῖος). Aegaeon could be a patronymic, i.e. "son of Aegaeus",  or it could instead mean "the man from Aegae".The name Hecatoncheires derives from the Greek ἑκατόν (hekaton, "hundred") and χείρ (cheir, "hand” or "arm"). Although the Theogony describes the three brothers as having one hundred hands (ἑκατὸν μὲν χεῖρες),  the collective name Hecatoncheires (Ἑκατόγχειρες), i.e. the Hundred-Handers, is never used. The Theogony once refers to the brothers collectively as "the gods whom Zeus brought up from the dark", otherwise it simply uses their individual names: Cottus, Briareus (or Obriareus) and Gyges.The Iliad does not use the name Hecatoncheires either, although it does use the adjective hekatoncheiros (ἑκατόγχειρος), i.e. "hundred-handed", to describe Briareus. It is possible that Acusilaus used the name, but the first certain usage is found in the works of the mythographers such as Apollodorus.Poseidon
Briareus/Aegaeon seems also closely connected with Poseidon. The name Aegaeon has associations with Poseidon. As noted above, Homer locates Poseidon's palace in Aegae. Poseidon was sometimes himself called Aegaeon, or Aegaeus (Αἰγαῖος), and Aegaeon could mean 'son of Aegaeus'.Homer says that Briareus/Aegaeon "is mightier than his father", but who Homer is referring to as the father is unclear. It has been sometimes supposed that contrary to Hesiod, who makes Uranus the father of Briareus, Cottus and Gyges, the father being referred to here is Poseidon, although this interpretation of Homer is uncertain at best.In the Theogony Briareus becomes the son-in-law of Poseidon, while Poseidon, whether regarded as the father of Briareus/Aegaeon, or not, is a central figure in the story told about the Hundred-Hander in the ‘’Iliad’’. Both are sea-gods with a special connection to Euboea. As noted above Poseidon was sometimes called Aegaeon, and it is possible that Aegaeon was an older cult-title for Poseidon, however according to Lewis Richard Farnell, it is more likely that Poseidon inherited the title of an "older Euboean sea-giant".As mentioned above, the scholiast on  Apollonius of Rhodes, tells us that according to Cinaethon, Aegeaon was defeated by Poseidon. Possibly then, Briareus/Aegaeon was an older (pre-Greek?) sea-god eventually displaced by Poseidon.According to a Corinthian legend, Briareus was the arbitrator in a dispute between Poseidon and Helios (Sun) over some land, deciding that the Isthmus of Corinth belonged to Poseidon and the acropolis of Corinth (Acrocorinth) to Helios.The Iliad
In a story that survives nowhere else, the Iliad briefly mentions Briareus (where it is said he was also called Aegaeon), referring to his having been summoned to Zeus' defense when "the other Olympians wished to put [Zeus] in bonds, even Hera and Poseidon and Pallas Athene." Achilles, while asking his mother the sea goddess Thetis to intercede with Zeus on his behalf, reminds her of a frequent boast of hers, that, at a time when the other Olympians wished to bind Zeus, she saved him by fetching the hundred-handed Briareus to Olympus:
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