das Muster
pattern
A repeating arrangement of lines, shapes, or colors on a surface, for example on fabric, paper, or tiles.
Das Hemd hat ein kariertes Muster.
The shirt has a checked pattern.

pattern / sample
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pattern
A repeating arrangement of lines, shapes, or colors on a surface, for example on fabric, paper, or tiles.
Das Hemd hat ein kariertes Muster.
The shirt has a checked pattern.

You can easily recognize the meaning of 'Muster' from the context. If it is about clothing or design, it means a repeated form. In a business context, it is a sample. If people are talking about behavior, it is a role model.
Das Kleid hat ein schönes Blumenmuster.
The dress has a beautiful floral pattern.
When 'Muster' describes an ideal example, it is often used in the fixed phrase 'ein Muster an' or 'ein Muster von' followed by a noun in the dative or genitive. This emphasizes an outstanding quality.
Dieser Schüler ist ein Muster an Fleiß und Disziplin.
This student is a model of diligence and discipline.
When it is about a design, 'Muster' is very often combined with adjectives that describe appearance. Typical examples are 'geblümt' (floral), 'gestreift' (striped), 'gepunktet' (polka-dotted), or 'geometrisch' (geometric).
Ich suche einen Vorhang mit einem dezenten, geometrischen Muster.
I'm looking for a curtain with a subtle geometric pattern.
In the meaning 'Probe' (sample), 'Muster' is often used with verbs from the business world. Common combinations are 'ein Muster anfordern' (to request a sample), 'ein Muster schicken' (to send a sample), or 'ein kostenloses Muster erhalten' (to receive a free sample).
Viele Firmen schicken auf Anfrage kostenlose Muster ihrer Produkte.
Many companies send free samples of their products upon request.
example
'das Beispiel' and 'das Muster' can both show how something should be or how something works. 'das Beispiel' is often used to explain a statement or show a behavior. 'das Muster' is more like a template or model that you use to make something. It can also be an ideal example of a quality or behavior. The words can be confused because both provide guidance. As a simple guide: an example explains something; a pattern or template often helps you make something in the same or a similar way.

Für den Brief benutzt Maria ein Muster aus dem Internet.
Maria uses a template from the internet for the letter.
Omar zeigt zu Hause ein Beispiel, damit seine Familie die Aufgabe versteht.
At home, Omar shows an example so that his family understands the task.