Gods

The NPCs found at the top of Olympus sitting in each throne. Interacting with these Gods will choose which god you will be the child of (which can be changed at anytime).

Children of Gods
Interacting with a God at Olympus will select which god you will be the child of. Each Child has a select few abilities that make them unique to any other. Receiving Custom Items, Armor or new Workstations (e.g. Dionysus' Cauldron).

You can find a more in depth list of the gods and their abilities here.