Look, the most basic way I'd break it down is that these three brothers split the cosmos after overthrowing their dad, Cronus, and drawing lots. Zeus got the sky and became the king of the gods, the big boss who throws lightning bolts and enforces order, however imperfectly. He's often portrayed as a ruler, a father figure, and, let's be honest, a bit of a womanizer whose romantic escapades are basically half of Greek mythology.
Hades got the Underworld, the realm of the dead. He's not the devil; he's more like the stern, introverted administrator of the afterlife. His domain is shadowy, silent, and final. He's bound to his realm, rarely leaves it, and is often associated with wealth (the riches under the earth) and a certain grim inevitability. His famous story is abducting Persephone, which is less about villainy and more about a lonely god claiming a queen for his silent kingdom.
Poseidon is the lord of the seas, earthquakes, and horses. He's tempestuous and moody, like the ocean itself—capable of calm serenity one moment and world-shattering fury the next. Sailors prayed to him, and he was known for his pride and quick temper, often holding grudges against mortals (like Odysseus) or entire cities. He represents raw, untamed natural power, in contrast to Zeus's political authority or Hades's quiet dominion over endings.