der Fetzen
rag / scrap
A torn-off, irregular piece of something, usually fabric, paper, or leather.
Er wischte den Tisch mit einem alten Fetzen sauber.
He wiped the table clean with an old rag.

rag / scrap
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rag / scrap
A torn-off, irregular piece of something, usually fabric, paper, or leather.
Er wischte den Tisch mit einem alten Fetzen sauber.
He wiped the table clean with an old rag.

The meaning of 'Fetzen' depends heavily on context. A physical piece (e.g., fabric), a piece of information (e.g., conversation), clothing (only in the plural), or drunkenness are the main distinctions.
Ich habe nur Fetzen des Liedes gehört, aber es gefiel mir.
I only heard snippets of the song, but I liked it.
To name the material of a 'Fetzen' (rag/scrap), German often uses a genitive construction ('ein Fetzen Stoff' — a scrap of fabric) or a compound noun ('ein Stofffetzen' — a fabric scrap).
Ein Fetzen Papier lag auf dem Boden.
A scrap of paper was lying on the floor.
In connection with information or sounds, 'Fetzen' (snippet/fragment) is often combined with verbs like 'aufschnappen' (to catch/overhear) or 'hören' (to hear). It emphasizes that you only caught a small, incomplete part.
Ich konnte durch die dünne Wand nur Fetzen ihres Streits aufschnappen.
Through the thin wall, I could only catch snippets of their argument.
When 'Fetzen' means clothing, it is colloquial and almost always used in the plural. The expression 'sich in die besten Fetzen werfen' means to put on one's nicest clothes.
Für die Hochzeit hat sie sich in ihre besten Fetzen geworfen.
For the wedding, she got dressed up in her best clothes.
The expression 'einen Fetzen haben' for 'to be very drunk' is colloquial and common especially in Austria and Bavaria. In other parts of Germany, it is understood less often.
Er war gestern auf dem Fest und hatte am Ende einen ziemlichen Fetzen.
He was at the festival yesterday and was pretty drunk by the end.
piece
'das Stück' and 'der Fetzen' can both mean a part of something larger. 'Stück' is neutral and can be clean, large, small, or regular in shape. 'Fetzen' is used mainly for something torn off and irregular, especially fabric, paper, or leather. A short part of a conversation or a melody can also be a 'Fetzen'. The words can be confused because a Fetzen is a kind of Stück. But 'Fetzen' has a stronger sense of tearing, damage, or incompleteness.

Nach dem Umzug fanden wir nur noch einen Fetzen vom alten Vorhang.
After the move, we found only a scrap of the old curtain.
David hat ein Stück Papier genommen und die Adresse notiert.
David took a piece of paper and wrote down the address.