
schmerzen
to ache
To cause or feel physical pain.
Nach dem langen Lauf schmerzt mein Knie.
After the long run, my knee aches.
to hurt / ache
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to ache
To cause or feel physical pain.
Nach dem langen Lauf schmerzt mein Knie.
After the long run, my knee aches.

to hurt
To cause mental or emotional pain; to offend or wound someone.
Seine abfälligen Worte haben mich sehr geschmerzt.
His derogatory words hurt me very much.
The verb 'schmerzen' (to hurt / ache) is derived directly from the noun 'der Schmerz' (pain). When something 'schmerzt' (hurts/aches), it causes pain. Both words are used for physical and emotional suffering.
Der Verlust seines Freundes bereitete ihm großen Schmerz.
The loss of his friend caused him great pain.
The case helps identify the type of pain. With physical pain, the person often appears in the dative ('Mir schmerzt der Rücken' — my back hurts). With emotional pain, the person appears in the accusative ('Sein Verrat schmerzt mich' — his betrayal hurts me).
Ihr schmerzte der Kopf von dem Lärm.
Her head ached from the noise.
The verb 'schmerzen' (to hurt / ache) can also be used impersonally with 'es' as the subject. This is typical in questions at the doctor's office when asking about the location of the pain.
Können Sie mir zeigen, wo genau es schmerzt?
Can you show me exactly where it hurts?
to injure / hurt / violate
Verletzen and schmerzen can both express emotional hurt. Verletzen tends to emphasize that words or actions cause the hurt. Schmerzen places greater emphasis on the emotional pain that is felt, which may last longer.

Die Erinnerung an seine abfälligen Worte schmerzt Maria noch heute.
The memory of his disparaging words still hurts Maria today.
Seine abfälligen Worte verletzten Maria tief.
His disparaging words deeply hurt Maria.