der Vers
line of verse
A single line in a poem, song lyrics, or another literary work written in metrical language.
Das Gedicht besteht aus vier Strophen mit je vier Versen.
The poem consists of four stanzas with four lines of verse each.

verse
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line of verse
A single line in a poem, song lyrics, or another literary work written in metrical language.
Das Gedicht besteht aus vier Strophen mit je vier Versen.
The poem consists of four stanzas with four lines of verse each.

The meaning of 'Vers' (verse) depends heavily on context. In literary analysis, it refers to a single line. In the context of songs, however, 'der erste Vers' (the first verse) can also mean the first stanza.
Dieser Vers hat genau zehn Silben.
This line of verse has exactly ten syllables.
When referring to a line of poetry, you often hear phrases like 'ein Gedicht in freien Versen' (a poem in free verse; without a fixed meter or rhyme) or 'ein Vers reimt sich auf einen anderen' (one line of verse rhymes with another).
Moderne Lyrik ist oft in freien Versen geschrieben.
Modern poetry is often written in free verse.
When 'Vers' (verse) is mentioned together with the name of a sacred book, e.g. the Bible or Quran, or with chapter and line numbers, it always means a short passage of text.
Er schlug die Bibel auf und las einen Vers vor.
He opened the Bible and read a verse aloud.
The use of 'Vers' (verse) for an entire stanza of a song is especially common in colloquial language and in the context of pop music. In literary studies, the term 'Strophe' (stanza) is used for this.
Lass uns nach dem zweiten Vers alle zusammen den Refrain singen.
Let's all sing the chorus together after the second verse.
section
'der Abschnitt' and 'der Vers' can both mean a part of a text. However, 'Abschnitt' is much more general: it can be a section in a factual text, a form, or a chapter. 'Vers' mainly fits poems, songs, or sacred texts. Learners may confuse the words because a verse is also a small part of a text. When talking about ordinary texts, 'Abschnitt' is more natural. When talking about a line or a numbered part in a poem, song, or religious text, 'Vers' is more precise.

Laura hat nach der Arbeit einen Vers aus dem Gedicht noch einmal gelesen.
After work, Laura read a verse from the poem again.
Im nächsten Abschnitt erklärt der Autor die wichtigsten Regeln.
In the next section, the author explains the most important rules.