das Stückchen
little piece
A small piece of something larger. It is the diminutive form of 'Stück' (piece).
Möchtest du ein Stückchen Schokolade probieren?
Would you like to try a little piece of chocolate?

little piece
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little piece
A small piece of something larger. It is the diminutive form of 'Stück' (piece).
Möchtest du ein Stückchen Schokolade probieren?
Would you like to try a little piece of chocolate?

The ending '-chen' is a diminutive form. It turns 'das Stück' (the piece) into the smaller 'Stückchen' (little piece) and signals that something is small, nice, or insignificant. All nouns ending in '-chen' are neuter and have the article 'das'.
Gib mir bitte nur ein kleines Stückchen vom Kuchen.
Please give me just a small little piece of the cake.
Whether a small part or a short distance is meant can be recognized from the context. In connection with food or materials, it means 'kleines Teil' (small part). In connection with verbs of movement like 'gehen' (to go/walk) or 'fahren' (to drive/ride), it means 'kurze Strecke' (short distance).
Kann ich noch ein Stückchen Käse haben?
Can I have another little piece of cheese?
In the meaning of 'kleines Teil' (small part), 'Stückchen' (little piece) is very often used with foods that can be divided. Typical combinations are 'ein Stückchen Kuchen' (a little piece of cake), 'ein Stückchen Schokolade' (a little piece of chocolate), or 'ein Stückchen Wurst' (a little piece of sausage).
Zum Kaffee gab es ein Stückchen Apfelkuchen.
There was a little piece of apple cake with the coffee.
When it is about a distance, 'ein Stückchen' (a little way) is often combined with the adverb 'weiter' (farther/onward) to express a small continuation of a movement or route.
Die Hütte ist nur noch ein Stückchen weiter den Berg hinauf.
The hut is only a little way farther up the mountain.
piece
'das Stück' and 'das Stückchen' both mean a part of something larger. The most important difference is size: 'Stückchen' is the diminutive form of 'Stück' and suggests something small. With cake, bread, or chocolate, you can say both, but 'ein Stückchen' sounds smaller and often a bit friendlier or more cautious. For distances, too, 'ein Stückchen' means only a short stretch. Learners may confuse the words because they look very similar. As a guide: 'Stück' is neutral, while 'Stückchen' emphasizes smallness.

Vor dem Termin esse ich nur ein kleines Stückchen Brot.
Before the appointment, I eat only a small piece of bread.
Zum Nachtisch nehme ich ein Stück Kuchen.
For dessert, I'll have a piece of cake.