The questions are posed: what is the meaning of the Hebrew God as compared to the meaning of god(s) in the Greek world, and what is the significance of the difference? In this interpretation I will assume that the word “meaning” means “significance” or “nature” – as meaning generally associates with personal judgment and is fundamentally impossible to summarize.
The Hebrew God initially was respected in a henotheistic fashion, being recognized as the most powerful or important god amongst many but with Hezekiah’s centralization of the cult at Jerusalem in the 8th century BCE the other idols were banished and the Tanakh was from that point on written to describe a solitary God, the only god, the creator of the universe and all that ever was. The Hebrew God essentially manifests as a ruthless, unreasoning and murderous tyrant who instills in his people a legacy of conquest by declaring that a large swathe of the Levant was to be divinely granted to them, lands which at the time were populated by many other peoples, nations which the Tanakh contends were destroyed by the Jews in ascension of their manifest destiny.
The Hebrew God is customarily referred to as being omnipotent (all powerful), omniscient (all knowing) and omnibenevolent (all loving) although this may very well be a contemporary perception as there are numerous internal contradictions to these claims within the Bible itself. Of particular absurdity is the latter claim that God is all loving, considering that it has been estimated by some scholars that he was personally responsible for at least 33,041,220 deaths in the Tanakh.
God is obsessed with sumptuary laws and the use and nature of our genitals, destroying those who do not obey seemingly random or nonsensical commandants. In Exodus 4:24-26 for example, God decides to kill Moses because he had not yet cut off the skin from his son’s penis and in Numbers 11:1 God sets the people on fire who had decided to eat meat, as he commanded them to only eat “mana.”
Later on in the history of the Jewish people, as the Assyrians expelled them from Jerusalem and the Bible was modified to explain this apparent injustice, God became a source of salvation and redemption involved in a cosmic struggle between the forces of good and evil, fated to return to redeem the righteous on “judgment day,” the end of times. This latter incarnation of God, a mysterious force that promises redemption to those who act righteously and unknowable barbarism to those who act poorly in the cosmic afterlife, is the more-or-less contemporary Hebrew God.
The conception of god(s) in the Greek world was one of greater polytheism with local polis-level examples of henotheism, centering around the 13 major gods Zeus (king of the gods), Hera, Poseidon, Apollo, Artemis, Aphrodite, Ares, Dionysus, Hephaestus, Athena, Hermes, Demeter, and Hestia. Unlike the God of the Hebrews the Greek gods tended to exhibit human qualities, especially as expressed in Homer’s Iliad and Odyssey: making mistakes, feuding, dying, battling each other, falling into love, showing empathy, taking part in family structures, forming relationships, having sex, laughing, crying, valuing comedy and picking sides in wars and politics. The gods mostly behaved, especially as depicted by Homer, as being spoiled socialites, all too willing to meddle in the affairs of the common man just for their own amusement or satisfaction, and having little regard for the sanctity of life through their careless indulgences. These Gods love mortals, as Aphrodite did with Adonis or Zeus with Leda, or might outright destroy a mortal who angered them, such as Dionysus did to King Pentheus of Thebes for mocking his religious craft. But the gods were not all too human, for they could exhibit magical powers, such as teleportation, elemental mastery, incredible strength, transmutation and illusion, to name a few.
The Greek gods could also be a source of great ideological inspiration and majesty, inspiring the virtue philosophies of Stoicism, Cynicism and Platonism by venerating the wisdom, courage, temperance and prudence of gods such as Zeus or Athena. In this sense the gods served as exemplary role models but not law givers, inspiring the people to act in a righteous way. While not inspiring the people as lead characters in didactic moral stories and dramas, the gods served as a source of entertainment in the epics, contrasting with the strength, incorruptibility and virtue of the hero.
While the gods were powerful, they did not possess unlimited power, as it was implied that even Zeus, king of the gods, could be inhibited or even killed by the combined efforts of other gods, only having true mastery over their individual portfolio of powers, ex. Hades had absolute domain of the underworld, Zeus over lightning and storm.
Ultimately the significant difference between the Hebrew God and the Greek gods was that that the absolute moral direction and unceasing tyranny of the former is surely missing in all of the latter. While the Hebrew God sought to bring about a cosmic order (at least late in the history of the Tanakh) between the forces of good and evil, moral absolutes, steering a divine people into a particular code of conduct by top-down commands and punishment, the Greek gods were players in the world who stood as role models to inspire the people on how to act by example in poetry and in the theatre. Fundamentally Greek mythology did not demand an especially divisive worldview, as the Hebrew God did, as it did not have a conception of sin, or of judging people on the merits of their perceived transgressions. While the Greek gods could be related to, or be perceived as extraordinary humans, the Hebrew God is an unknowable sociopath of capricious insanity which at one moment preaches love and in the next eradicates entire cities of people without pause or reason. Ultimately the nature of the Hebrew God can be lent to the environment to which it was created: from the culture of a primitive hill tribe torn between the more literate and cosmopolitan imperial forces of Assyria and Egypt. The Greeks, another cosmopolitan and cultured people (by relative standards) would come to create gods which fancied wisdom, creativity, love, poetry, courage, beauty, song, dance and merriment, aspects which they thought were the touchstones of humanity. The Jews, too prone to violence and indecency, were unable to raise themselves from their barbaric infancy and instead resigned to be ruled by a madman.
 Exodus 20:3, 5
 Hezekiah’s Reforms and
the Revolt against Assyria. The Foundation for Biblical Archaeology. http://www.tfba.org/articlespreview.php?articleid=10
 Isaiah 43:10
 Cruelty and Violence in the Bible. Skeptic’s Annotated Bible. http://skepticsannotatedbible.com/cruelty/long.html
 Ezekiel 47:13-20
 Can God do anything? Skeptic’s Annotated Bible. http://skepticsannotatedbible.com/contra/cando.html
 Does God know and see everything? Skeptic’s Annotated Bible. http://skepticsannotatedbible.com/contra/knows.html
 Does God love everyone? Skeptic’s Annotated Bible. http://skepticsannotatedbible.com/contra/god_hates.html
 How many has God killed? Dwindling in Unbelief. http://dwindlinginunbelief.blogspot.com/2007/01/how-many-has-god-killed-complete-list.html
 Who Wrote the Bible?. First broadcast 25 December 2004 by Channel 4. Directed by Polly Morland and written by Robert Beckford.
 Dionysus – Wine God. About.com: Ancient/Classical History. http://ancienthistory.about.com/od/dionysusmyth/a/Dionysus.htm
 The Ethics of Athena. The Encyclopedia of the Goddess Athena. http://www.goddess-athena.org/Encyclopedia/Ethics/index.htm