die Musterung
patterning
The repeating design, ornament, or pattern on a surface, for example on fabric, wallpaper, or an animal's skin.
Das Hemd hat eine dezente karierte Musterung.
The shirt has a subtle checkered patterning.

patterning / medical examination
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patterning
The repeating design, ornament, or pattern on a surface, for example on fabric, wallpaper, or an animal's skin.
Das Hemd hat eine dezente karierte Musterung.
The shirt has a subtle checkered patterning.

The word 'Musterung' (patterning / medical examination) is derived from 'das Muster' (the pattern / sample). A 'Muster' can be a design (meaning 1) or a test specimen (a 'sample' human is examined, meaning 2).
Das Muster des Teppichs passt gut zur Musterung der Vorhänge.
The pattern of the carpet goes well with the patterning of the curtains.
The two meanings are very different. If it is about fabric, design, animals, or surfaces, it refers to the pattern. If it is about the military, compulsory service, or doctors, it refers to the fitness examination.
Die Schlange hatte eine auffällige, zickzackförmige Musterung.
The snake had a striking zigzag patterning.
For the design meaning, adjectives that describe the pattern are often used, e.g. 'eine feine Musterung' (a fine patterning), 'eine geometrische Musterung' (a geometric patterning), or 'eine natürliche Musterung' (a natural patterning).
Der Schmetterling hat eine wunderschöne Musterung auf den Flügeln.
The butterfly has beautiful patterning on its wings.
In a military context, you go 'zur Musterung' (to the medical examination) or are 'zur Musterung einberufen' (called up for the medical examination). The result is that you are classified as 'tauglich' (fit) or 'untauglich' (unfit).
Viele junge Männer fürchteten sich früher vor der Musterung.
In the past, many young men were afraid of the military medical examination.
design
'das Design' and 'die Musterung' can both describe the appearance of a surface. However, 'Design' is more general and refers to the overall deliberate design, for example the shape, colors, and function of a product. 'Musterung' means a repeated pattern or marking on a surface, such as on fabric, wallpaper, or fur. Learners may confuse the words because a 'Musterung' can be part of a 'Design'. If you only mean stripes, dots, or other repeated shapes, 'Musterung' is more precise. If you mean the whole design, 'Design' is more natural.

Die Musterung des Stoffes besteht aus kleinen blauen Punkten.
The patterning of the fabric consists of small blue dots.
Das Design der Lampe passt gut zu den hellen Möbeln im Wohnzimmer.
The design of the lamp goes well with the light-colored furniture in the living room.