das Heft
notebook
A thin book made of bound paper pages for writing or drawing, often used at school.
Bitte schreib die Vokabeln in dein Heft.
Please write the vocabulary in your notebook.

notebook / issue / handle
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notebook
A thin book made of bound paper pages for writing or drawing, often used at school.
Bitte schreib die Vokabeln in dein Heft.
Please write the vocabulary in your notebook.

The noun 'Heft' is derived from the verb 'heften' (to staple/fasten), which means 'zusammenfügen' (to join together). So a 'Heft' is something in which paper pages are stapled or bound together, which explains its meaning as a school notebook or magazine issue.
Die losen Blätter wurden zu einem Heft zusammengeheftet.
The loose sheets were stapled together into a notebook.
To distinguish between a school notebook and a magazine issue, pay attention to the context. Words like 'Schule' (school), 'schreiben' (to write), or 'Hausaufgaben' (homework) point to a notebook. Words like 'lesen' (to read), 'Kiosk' (kiosk/newsstand), or a topic like 'Mode' (fashion) point to a magazine.
Für den Matheunterricht brauchst du ein kariertes Heft.
You need a squared notebook for math class.
The idiom 'das Heft in der Hand haben' (to be in control) or 'behalten' (to keep control) is a fixed expression. It means to have control or leadership over a situation.
Obwohl die Diskussion chaotisch war, behielt die Moderatorin das Heft in der Hand.
Although the discussion was chaotic, the moderator kept control.
The meaning 'Griff' (handle) is rare and is used almost only in connection with tools or historical weapons. You can recognize it from the context of words like 'Messer' (knife), 'Schwert' (sword), or 'Dolch' (dagger).
Das alte Schwert hatte ein Heft aus reinem Silber.
The old sword had a handle made of pure silver.
book
'das Buch' and 'das Heft' can both consist of paper pages and be used for reading or writing. 'Buch' usually means a larger or sturdier work with content to read. 'Heft' is often thinner and is used at school or in everyday life for writing. It can also be an issue of a magazine. Learners may confuse the words because both can look like small bound paper works. If you are taking notes, 'Heft' is more natural. If you are reading a complete work, 'Buch' is more natural.

Am Morgen schreibt Tom die neuen Wörter in sein Heft.
In the morning, Tom writes the new words in his notebook.
Das Buch für die Prüfung liegt schon auf dem Schreibtisch.
The book for the exam is already on the desk.