Your plane, Oceanic Airlines Flight 815, crash lands with 70 other people. You aren’t in Kansas anymore. You are stateless. The survivors each pick out unique sections of the beach for themselves and declare the areas as their new homes. There’s no city hall to assign or keep track of these land claims (or rather, these new home addresses). IPv6 stateless autoconfiguration is like this. Instead of a device being assigned an address, they first listen for IPv6 router advertisements to announce what network they are on. This gives them the subnet portion of the IPv6 address, they just need a unique host portion, which is based off the device’s MAC address. An IPv6 host using stateless autoconfiguration proposes an address that will probably be unique since it is based on that shared network prefix and its MAC address. It then does a duplicate address detection to make sure no one else on that network is using the same.
But let’s say you crash land in New York with 70 other people. If survivors try to pick out unique apartments for themselves in NYC and try to move in, they will probably be killed or taken to jail. Why? Because New York is stateful. Somewhere, someone is maintaining state information to eliminate conflicts, to handle apartment leases, to renew leases. IPv6 stateful autoconfiguration is like this, with a DHCPv6 server maintaining state information.
Stateless has no memory of the past. Every transaction is performed as if it were being done for the first time. Stateless is plug and play.
Stateful keeps lists. It retains information for future use. There is more control.