
Vorgang
process
A sequence of connected events or actions; a process or procedure.
Der gesamte Vorgang von der Bestellung bis zur Lieferung dauerte nur zwei Tage.
The entire process from ordering to delivery took only two days.
process / occurrence
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process
A sequence of connected events or actions; a process or procedure.
Der gesamte Vorgang von der Bestellung bis zur Lieferung dauerte nur zwei Tage.
The entire process from ordering to delivery took only two days.

occurrence
A particular incident or event that attracts attention.
Die Polizei untersucht den seltsamen Vorgang von letzter Nacht.
The police are investigating the strange occurrence from last night.

case file
In a bureaucratic context, a file or dossier that contains all documents relating to a specific case or topic.
Der zuständige Sachbearbeiter hat den Vorgang zur Prüfung erhalten.
The responsible case officer has received the case file for review.
'Vorgang' (process/occurrence) consists of the prefix 'vor' (before/in front of) and the noun 'Gang' (course/walk, from 'gehen' — to go). It describes something that takes place or 'vor sich geht' (goes on/happens).
Die Fotosynthese ist ein komplexer biologischer Vorgang.
Photosynthesis is a complex biological process.
You can recognize the meaning of 'Vorgang' (process/occurrence) from the context. In a technical or scientific context, it means 'process'. In everyday language or with the police, it describes an 'occurrence'. In an office or at a government authority, it means a 'file' or 'case file'.
Die Gärung von Wein ist ein chemischer Vorgang.
The fermentation of wine is a chemical process.
In the meaning of 'Prozess' (process) or 'Ablauf' (procedure/course), 'Vorgang' (process) is often combined with adjectives such as 'automatisch' (automatic), 'komplex' (complex), 'natürlich' (natural), or 'chemisch' (chemical).
Das Speichern der Daten ist ein automatischer Vorgang.
Saving the data is an automatic process.
The meaning 'Akte' (file) or 'Fall' (case) is typical of office and administrative language (official German). In this context, a Vorgang is often 'angelegt' (opened/created), 'bearbeitet' (processed), or 'abgeschlossen' (closed/completed).
Die Sachbearbeiterin hat für Ihre Beschwerde einen neuen Vorgang angelegt.
The case officer has opened a new case file for your complaint.
case / fall
Der Fall and der Vorgang can refer to the same matter involving a citizen. Der Fall tends to mean the underlying situation or matter, whereas der Vorgang refers to the administrative file with its documents. „Fall“ fits the matter itself, while „Vorgang“ is more appropriate for its processing at a government office.

Der Vorgang der Familie liegt mit allen Unterlagen auf dem Schreibtisch der Sachbearbeiterin.
The family’s case file, together with all the documents, is on the caseworker’s desk.
Der Fall der Familie wird nächste Woche von einer Sachbearbeiterin geprüft.
A caseworker will review the family’s case next week.