
der Schmerz
pain
An unpleasant physical sensation caused by an injury or illness.
Nach der Operation hatte er starke Schmerzen im Bein.
After the operation, he had severe pain in his leg.
pain
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pain
An unpleasant physical sensation caused by an injury or illness.
Nach der Operation hatte er starke Schmerzen im Bein.
After the operation, he had severe pain in his leg.

pain
Deep emotional suffering caused by grief, loss, or disappointment.
Der Schmerz über den Tod ihres Freundes war kaum zu ertragen.
The pain over her friend's death was almost unbearable.
Physical pain is often used in the plural in German ('Schmerzen'), while emotional suffering is almost always in the singular ('der Schmerz'). This usually makes the meaning easy to recognize.
Sie hat seit gestern starke Schmerzen im Rücken.
She has had severe back pain since yesterday.
For physical complaints, the plural form 'die Schmerzen' (pain) is used very frequently, even when only one part of the body is affected. The question 'Wo haben Sie Schmerzen?' (Where do you have pain?) is typical at the doctor's.
Ich habe seit Tagen Schmerzen im Knie.
I have had pain in my knee for days.
'Schmerz' (pain) is often combined with a body part to form a new word that specifies the type of pain. Examples are 'Kopfschmerzen' (headache), 'Bauchschmerzen' (stomachache), or 'Rückenschmerzen' (back pain).
Nach der langen Autofahrt hatte er starke Rückenschmerzen.
After the long car ride, he had severe back pain.
Emotional pain is often combined with verbs such as 'empfinden' (to feel/experience) or 'fühlen' (to feel). The cause of the pain is often expressed with the preposition 'über' (+ accusative).
Er fühlte einen tiefen Schmerz über den Verlust seines Freundes.
He felt deep pain over the loss of his friend.
suffering
Both words can refer to intense physical distress. Schmerz mainly names the specific unpleasant sensation, while Leid describes the broader condition, including sorrow or misfortune. Use „Schmerz“ for the sensation and „Leid“ for the entire distressing experience.

Der Schmerz im Bein des Patienten war nach dem Unfall besonders stark.
The pain in the patient's leg was particularly severe after the accident.
Das Leid des Patienten nach dem Unfall war für die ganze Familie schwer zu ertragen.
The patient's suffering after the accident was hard for the whole family to bear.