Domains come in multiple levels, each with varied degrees of specialization. Lesser domains are the most specialized and likely most commonly acquired, while the Greater domains are the opposite. Any god may claim any Greater, Moderate, or Lesser domain regardless of if it has already been claimed by another god. This is done simply by a god taking interest in that domain over several days.
While Greater domains tend to be wider in scope, Lesser domains exert greater control over the limited element. A god of Dragons (a Moderate domain) would have more control over dragons than a god of Life (a Greater domain), but a god of Chromatic Dragons (a Moderate domain) would have greater control over Chromatic Dragons than the god of Dragons, and a god of Red Dragons (a Lesser Domain) would have greater control over those creatures than any other mentioned god.
Greater Domains are some of the more powerful domains available. They include the basic elements, concepts that are essential to civilization, and more abstract things like Time and Void. Remember, with great power comes great responsibility.
Moderate Domains are more specific than greater domains allowing for wider control over a certain aspect of existence such as weather and dragons.
Lesser Domains are the most specialized types of domains in the game, allowing the god or goddess who holds it unrivaled influence over that particular aspect of reality.
A list of example domains of all three levels, for reference. These are by no means the only domains available, nor must these domains actually be present in the game.
Air, Balance, Chaos, Creation, Darkness, Death, Destruction, Earth, Evil, Fate, Fire, Good, Harmony, Ice, Ki, Knowledge, Law, Life, Light, Magic, Nature, Order, Peace, Secrets, Time, Void, War, Water
Aberrations, Animals, Bravery, Civilization, Conquest, Corruption, Decay, Diseases, Dragons, Dreams, Fey, Gravity, Healing, Honor, Invention, Justice, Language, Luck, Madness, Mercy, Metal, Moon, Music, Necromancy, Ocean, Passion, Pestilence, Plant, Protection, Psionics, Purification, Rebirth, Renewal, Retribution, River, Sky, Slaughter, Stars, Storm, Strategy, Strength, Sun, Travel, Trickery, Truth, Undead, Weather.
Athletics, Blacksmiths, Blue Dragons, Caverns, Chromatic Dragons, Cities, Courage, Day, Deception, Dwarves, Elves, Endurance, Envy, Evil Dragons, Fear, Fighters, Force, Forest, Gold Dragons, Greed, Halflings, Harvest, Hatred, History, Illusion, Insight, Joy, Kobolds, Lightning, Love, Lust, Machinery, Meditation, Mountains, Night, Pain, Pleasure, Poison, Pride, Revelry, Rogues, Runes, Scrying, Sea, Sight, Sleep, Song, Stealth, Suffering, Teleportation, Trade, Traps, Trees, Tyrants, Vanity, Vengeance, Victory, Wind, Wizards, Wrath