der Anrufer
caller
A person who makes a telephone call.
Ein unbekannter Anrufer hat sich nach Ihnen erkundigt.
An unknown caller asked about you.

caller / appellant
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caller
A person who makes a telephone call.
Ein unbekannter Anrufer hat sich nach Ihnen erkundigt.
An unknown caller asked about you.

'Der Anrufer' (the caller/appellant) is derived from the verb 'anrufen' (to call; to appeal to). The ending '-er' indicates a male person who performs the action. The female form is 'die Anruferin' (the female caller/appellant).
Die Anruferin wollte mit der Chefin sprechen.
The female caller wanted to speak with the boss.
In the context of phone calls, 'Anrufer' (caller) is often combined with adjectives like 'unbekannt' (unknown), 'anonym' (anonymous), or 'der erste/nächste' (the first/next). 'Die Nummer des Anrufers' (the caller's number) is also a common phrase.
Die Nummer des Anrufers wurde auf dem Display nicht angezeigt.
The caller's number was not shown on the display.
This meaning belongs to the technical language of the justice system. You can recognize it because the context is always a court, an authority, or a formal proceeding. Words like 'Gericht' (court), 'Beschwerde' (complaint/appeal), or 'Verfahren' (proceeding) are clear signals.
Das Gericht gab dem Anrufer in seinem Urteil recht.
The court found in favor of the appellant in its judgment.
plaintiff
'der Kläger' and 'der Anrufer' can both be people who turn to a court in a legal sense. However, 'der Kläger' files a lawsuit against another person or party in a civil case. In this legal usage, 'der Anrufer' is someone who appeals to a court or higher authority so that a decision can be reviewed. In everyday language, 'Anrufer' usually simply means a person on the phone; that is not meant here. The risk of confusion arises because both take legal action. 'Kläger' fits a lawsuit against someone; 'Anrufer' fits the review of a decision by a higher authority.

Der Anrufer möchte, dass die höhere Instanz die Entscheidung noch einmal prüft.
The appellant wants the higher authority to review the decision again.
Der Kläger bringt neue Unterlagen mit, damit das Gericht den Fall prüfen kann.
The plaintiff brings new documents so the court can review the case.