
der Magen
stomach
An internal organ in the upper abdomen that digests the food that has been eaten.
Nach dem schweren Essen tut mir der Magen weh.
After the heavy meal, my stomach hurts.
stomach
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stomach
An internal organ in the upper abdomen that digests the food that has been eaten.
Nach dem schweren Essen tut mir der Magen weh.
After the heavy meal, my stomach hurts.

stomach
A way of referring to the stomach area as the center of feelings such as discomfort, fear, or excitement.
Bei dem schrecklichen Anblick drehte sich mir der Magen um.
At the terrible sight, my stomach turned.

to weigh heavily on someone
Something that occupies or burdens someone greatly and causes worry.
Die ungelöste Aufgabe liegt ihm immer noch schwer im Magen.
The unresolved task is still weighing heavily on him.
When the stomach is causing pain, the person who has the pain is often expressed with a dative pronoun. The structure is then: 'Mir tut der Magen weh.' (My stomach hurts.)
Dem Patienten tat nach der Operation der Magen weh.
The patient's stomach hurt after the operation.
Common phrases related to eating and drinking are 'auf nüchternen Magen' (on an empty stomach/without having eaten beforehand), 'ein leerer Magen' (an empty stomach), or 'ein voller Magen' (a full stomach).
Man sollte Medikamente nicht auf nüchternen Magen einnehmen.
You shouldn't take medication on an empty stomach.
The stomach is often used metaphorically for feelings. Positive excitement is described with 'Schmetterlinge im Magen haben' (to have butterflies in one's stomach), discomfort or nervousness with 'ein flaues Gefühl im Magen haben' (to have an uneasy feeling in one's stomach).
Vor jeder Prüfung habe ich ein flaues Gefühl im Magen.
Before every exam, I have an uneasy feeling in my stomach.
In the expression 'jemandem schwer im Magen liegen' (to weigh heavily on someone), the problem is the subject of the sentence. The person who is worried stands in the dative.
Die Entscheidung, umzuziehen, liegt ihr immer noch schwer im Magen.
The decision to move is still weighing heavily on her.
belly / stomach
Bauch refers to the entire front part of the body between the chest and the pelvis. Magen is a specific digestive organ in the upper abdomen. Bauch fits general or imprecisely located discomfort; when the organ or its digestive function is meant, Magen is the right word.

Nach dem schweren Essen tut mir der Magen weh.
My stomach hurts after the heavy meal.
Nach dem Sturz tut mir der ganze Bauch weh.
After the fall, my entire abdomen hurts.