"Anguish" vs. "sadness": unpacking emotions beyond the blue

What is similar?

Both refer to negative emotions. Both can be experienced as a response to distressing events. Both words can describe internal emotional states.

What is different?

Anguish implies a more intense, acute level of suffering and distress than sadness. Sadness can be a more general and less intense emotion compared to the severe pain that anguish suggests. Anguish often suggests a combination of emotional and psychological pain, whereas sadness is more purely emotional.

Which one is more common?