der Auszug
move-out
Leaving an apartment or house in order to live somewhere else.
Der Auszug aus unserer alten Wohnung war anstrengender als gedacht.
The move-out from our old apartment was more exhausting than expected.

move-out / excerpt / statement
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move-out
Leaving an apartment or house in order to live somewhere else.
Der Auszug aus unserer alten Wohnung war anstrengender als gedacht.
The move-out from our old apartment was more exhausting than expected.

“Der Auszug” is the noun form of the separable verb “ausziehen” (to move out). The meaning “to leave an apartment” comes directly from this verb.
Wir ziehen nächsten Monat aus; der Auszug wird am ersten Samstag sein.
We're moving out next month; the move-out will be on the first Saturday.
You can recognize the meaning of “Auszug” from the context. If it is about an “Wohnung” (apartment), it means leaving. If it is about a “Buch” (book) or a “Text” (text), it means a section. In the context of “Bank” (bank) or “Konto” (account), it means a bank statement.
Der Auszug aus der alten Wohnung ist für den 31. Mai geplant.
The move-out from the old apartment is planned for May 31.
When describing leaving an apartment, the preposition “aus” is used to name the place that someone is leaving.
Der Auszug aus dem Haus seiner Eltern fiel ihm schwer.
The move-out from his parents' house was hard for him.
In the context of texts or music, typical verbs are “lesen” (to read), “hören” (to hear/listen to), “zitieren” (to quote), or “vorlesen” (to read aloud). The source is often given with “aus” (from).
Sie las einen Auszug aus ihrem neuen Roman.
She read an excerpt from her new novel.
In banking, “Auszug” is almost always a short form of “der Kontoauszug” (bank statement). It is used when the context makes it clear that the topic is finances.
Am Automaten können Sie sich die Auszüge der letzten 90 Tage ziehen.
At the machine, you can get the statements from the last 90 days.
section
'der Abschnitt' and 'der Auszug' can both mean a part of a longer text. 'Abschnitt' refers to a part within the text, for example a paragraph or a chapter. It belongs to the structure of the whole text. 'Auszug', on the other hand, means a selected short part that is taken from a longer text, book, or piece of music and shown or quoted separately. Learners may confuse the words because both talk about parts of texts. As a guide: within the text itself there are 'Abschnitte' (sections); when you read aloud, copy, or print only one part from it, it is an 'Auszug' (excerpt).

In der Zeitung stand ein kurzer Auszug aus dem neuen Roman.
The newspaper printed a short excerpt from the new novel.
Bitte lies den zweiten Abschnitt noch einmal langsam vor.
Please read the second section aloud again slowly.