die Schrift
handwriting
The personal, individual way of writing by hand; handwriting.
Ich kann seine Schrift kaum lesen, er kritzelt so.
I can barely read his handwriting; he scribbles so much.

writing / script
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handwriting
The personal, individual way of writing by hand; handwriting.
Ich kann seine Schrift kaum lesen, er kritzelt so.
I can barely read his handwriting; he scribbles so much.

'Die Schrift' belongs to the word family of the verb 'schreiben' (to write). All meanings have to do with the written word, whether by hand, as a system, or as a text.
Schon als Kind hatte er eine sehr ordentliche Schrift.
Even as a child, he had very neat handwriting.
When 'Schrift' (handwriting) means handwriting, it is often described with adjectives such as 'leserlich' (legible), 'unleserlich' (illegible), 'schön' (beautiful/neat), or 'deutlich' (clear). You can 'lesen' (read) or 'entziffern' (decipher) someone's handwriting.
Seine Schrift ist so unleserlich, dass ich den Brief nicht entziffern kann.
His handwriting is so illegible that I can't decipher the letter.
When referring to a writing system, 'Schrift' (script) is often specified by a culture or a name. Examples include 'die arabische Schrift' (the Arabic script), 'die kyrillische Schrift' (the Cyrillic script), or 'die chinesische Schrift' (Chinese writing/characters).
Für meinen Russischkurs muss ich die kyrillische Schrift lernen.
For my Russian course, I have to learn the Cyrillic script.
In the meaning of 'published text', 'Schrift' (writing/text) is used mainly in academic and formal contexts for a treatise or tract. Typical verbs are 'verfassen' (to write/compose) or 'veröffentlichen' (to publish).
Die Historikerin hat eine wichtige Schrift über das Mittelalter veröffentlicht.
The historian published an important text on the Middle Ages.
In the context of computers, design, or printing, 'Schrift' (font/typeface) means a typeface or font. Typical verbs here are 'auswählen' (to select), 'ändern' (to change), or 'installieren' (to install).
Kannst du für das Dokument bitte eine andere Schrift auswählen?
Could you please select a different font for the document?
In the religious meaning, the fixed expression 'die Heilige Schrift' (Holy Scripture) is used almost exclusively to refer to the Bible.
Im Gottesdienst las der Priester aus der Heiligen Schrift vor.
During the church service, the priest read from Holy Scripture.
book
'das Buch' and 'die Schrift' can both be a published text. However, 'Buch' is much more common for a complete work that you read, buy, or borrow. In this meaning, 'Schrift' sounds more formal and often refers to a shorter academic, religious, or informative text. Learners may confuse the words because both can refer to texts. In everyday language, people usually say 'Buch'. 'Schrift' fits better when the text is meant as a document or treatise.

Der Professor empfiehlt eine kurze Schrift über die Geschichte der Stadt.
The professor recommends a short text about the history of the city.
Jana liest zur Vorbereitung ein Buch über italienische Küche.
Jana reads a book about Italian cuisine to prepare.