processing / adaptation
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processing
The process in which something (e.g., an application, a text, a material) is checked, changed, or developed further.
Die Bearbeitung Ihres Antrags kann einige Wochen dauern.
The processing of your application may take a few weeks.
'Bearbeitung' (processing/adaptation) is a noun derived from the verb 'bearbeiten' (to work on/edit/process). The verb means to work on something in order to change it or complete it. The ending '-ung' turns the verb into a noun that describes the process or the result.
Ich muss den Text noch einmal bearbeiten.
I have to edit the text one more time.
In administrative contexts, 'Bearbeitung' (processing) is often combined with words like 'Antrag' (application), 'Auftrag' (order/assignment), or 'Anfrage' (inquiry). A common phrase is that something 'in Bearbeitung ist' (is being processed / is in progress).
Ihr Visum ist aktuell in Bearbeitung.
Your visa is currently being processed.
This meaning is found in the context of art, music, or literature. Typical adjectives are 'musikalisch' (musical), 'literarisch' (literary), or 'modern' (modern). It always refers to the new version of an already existing work.
Diese Rockband ist für ihre Bearbeitungen klassischer Stücke bekannt.
This rock band is known for its arrangements of classical pieces.
version
'die Version' and 'die Bearbeitung' can both refer to a form of something that has been changed. 'Version' mainly says that there is a particular version alongside other versions, for example with a text, program, or product. 'Bearbeitung' puts more emphasis on something being checked, changed, or adapted. In art, music, or literature, 'Bearbeitung' can also mean the finished adapted work. The words can be confused because a 'Bearbeitung' is often also a 'Version'. In practical terms: 'Version' fits when you are comparing different versions. 'Bearbeitung' fits when the process of changing something, or the adaptation itself, is important.
Die Bearbeitung des Antrags dauert noch einige Tage.
Processing the application will take a few more days.
Für die Präsentation nimmt Lisa die kurze Version des Textes.
For the presentation, Lisa uses the short version of the text.