der Abschnitt
section
A part of a text, such as a chapter, paragraph, or thematically connected block.
Bitte lesen Sie den dritten Abschnitt auf Seite 45.
Please read the third section on page 45.

section
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section
A part of a text, such as a chapter, paragraph, or thematically connected block.
Bitte lesen Sie den dritten Abschnitt auf Seite 45.
Please read the third section on page 45.

'Abschnitt' comes from the verb 'abschneiden' (to cut off). So an 'Abschnitt' is literally a part that has been 'cut off' or separated from a larger whole. This idea connects all of its meanings.
Schneiden Sie bitte einen Abschnitt vom Papier ab.
Please cut off a section of the paper.
The context reveals the meaning: if it's about a 'Buch' (book) or a 'Text' (text), it means a part of the text. With 'Straße' (road) or 'Weg' (path), it refers to a section of a route. With 'Leben' (life) or 'Geschichte' (history/story), it means a phase of time.
Dieser Abschnitt des Buches ist besonders spannend.
This section of the book is especially exciting.
In the context of texts, 'Abschnitt' (section) is often combined with verbs like 'lesen' (to read), 'zitieren' (to quote), or 'überspringen' (to skip), and adjectives like 'kurz' (short), 'lang' (long), or 'wichtig' (important).
Ich habe den letzten Abschnitt nicht verstanden.
I didn't understand the last section.
When it comes to forms, tickets, or vouchers, the 'Abschnitt' is the part that you detach and often keep as proof or a receipt. Typical verbs here are 'abtrennen' (to detach) and 'aufbewahren' (to keep).
Bitte trennen Sie den unteren Abschnitt ab und schicken Sie ihn an uns zurück.
Please detach the lower section and send it back to us.
part
'der Teil' and 'der Abschnitt' both mean something that belongs to a larger whole. 'Teil' is more general and can mean almost any piece or area of a whole. 'Abschnitt' works especially well when something is clearly limited or bounded: a part of a text, a route, a period of time, or a detachable part of a form. Learners may confuse the words because an 'Abschnitt' is often also a 'Teil'. But not every 'Teil' is an 'Abschnitt'. When the boundary or sequence is important, 'Abschnitt' sounds more natural.

Im letzten Abschnitt des Textes erklärt die Autorin ihre Meinung.
In the last section of the text, the author explains her opinion.
Ein Teil des Kuchens bleibt für die Gäste am Abend.
Part of the cake is left for the guests in the evening.