die Wunde
wound
An injury to the body in which the skin or tissue is damaged by an external force.
Der Arzt hat die Wunde gereinigt und einen Verband angelegt.
The doctor cleaned the wound and applied a bandage.

wound
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wound
An injury to the body in which the skin or tissue is damaged by an external force.
Der Arzt hat die Wunde gereinigt und einen Verband angelegt.
The doctor cleaned the wound and applied a bandage.

The context tells you whether a physical or emotional injury is meant. Words like 'Arzt' (doctor), 'Haut' (skin), or 'bluten' (to bleed) point to the physical wound, while 'Herz' (heart), 'Seele' (soul), or 'Verrat' (betrayal) refer to the figurative, emotional meaning.
Er hat eine kleine Wunde am Knie, die aber nicht schlimm ist.
He has a small wound on his knee, but it's not serious.
In a medical context, a wound is often 'versorgt' (treated), 'gereinigt' (cleaned), 'desinfiziert' (disinfected), or 'genäht' (stitched). When it gets better, you say that the wound 'heilt' (heals).
Die Wunde muss regelmäßig desinfiziert werden, damit sie gut heilt.
The wound has to be disinfected regularly so that it heals well.
The emotional meaning is often used in fixed expressions. Well-known ones include 'alte Wunden aufreißen' (to reopen old wounds) or the proverb 'Die Zeit heilt alle Wunden' (time heals all wounds).
Das Gespräch über die Vergangenheit hat nur alte Wunden aufgerissen.
The conversation about the past only reopened old wounds.
pain
'der Schmerz' and 'die Wunde' can both be meant physically or emotionally. 'Schmerz' is the unpleasant feeling you sense, for example after an injury or in grief. 'Wunde' is the injury itself, that is, a damaged place on the body. Figuratively, 'Wunde' can also be an emotionally painful point. The words can be confused because a wound often causes pain. The important point is: the wound is the injury; the pain is the feeling.

Die Ärztin reinigt die Wunde, damit sie sich nicht entzündet.
The doctor cleans the wound so that it does not become infected.
Nach dem Sturz hatte Tom einen starken Schmerz im Knie.
After the fall, Tom had severe pain in his knee.