‘Calm down’ means, to become relaxed, quiet, less angry or upset with someone or something.
Example: “After the fight and the police arrived, everything seemed to ‘calm down’.”
‘Settle down’ – has two meanings; it can mean similar to above. To become calm or composed. It can also mean: To begin living a stable normal life.
Example: “After all the women he went out with. He met Gloria and settled down”.