
erscheinend
appearing
Becoming visible; in the process of emerging.
Der am Horizont erscheinende Vollmond tauchte die Landschaft in ein fahles Licht.
The full moon appearing on the horizon bathed the landscape in a pale light.
appearing / forthcoming
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appearing
Becoming visible; in the process of emerging.
Der am Horizont erscheinende Vollmond tauchte die Landschaft in ein fahles Licht.
The full moon appearing on the horizon bathed the landscape in a pale light.

forthcoming
In the process of being published, usually in reference to books, magazines, or other media.
Die nächste Woche erscheinende Ausgabe des Magazins enthält ein Interview mit dem Kanzler.
The issue of the magazine appearing next week contains an interview with the chancellor.
'Erscheinend' (appearing) is the present participle of the verb 'erscheinen' (to appear). It describes an action that is currently taking place or in progress and is used like an adjective.
Die am Himmel erscheinenden Sterne waren wunderschön.
The stars appearing in the sky were beautiful.
This word is used almost exclusively as an adjective before a noun (attributively). Predicative use, such as 'Der Mond ist erscheinend' (The moon is appearing), is uncommon and sounds unnatural.
Der auf der Bühne erscheinende Künstler wurde mit Applaus begrüßt.
The artist appearing on stage was greeted with applause.
The meaning depends on the noun. In connection with visible things (sun, person), it means 'auftauchend' (emerging/appearing). In connection with media (book, article), it means 'veröffentlicht werdend' (being published).
Der plötzlich auf der Straße erscheinende Hund sorgte für eine Vollbremsung.
The dog suddenly appearing in the street caused an emergency stop.
In the context of publications, 'erscheinend' (appearing/forthcoming) is often combined with adverbs of time such as 'bald' (soon), 'demnächst' (soon/shortly), 'neu' (newly), or 'wöchentlich' (weekly).
Die wöchentlich erscheinende Zeitung hat eine hohe Auflage.
The weekly newspaper has a high circulation.
occurring
„Auftretend“ and „erscheinend“ can both describe a problem or symptom. „Erscheinend“ draws more attention to something becoming visible or appearing at that moment, while „auftretend“ is more neutral and also refers to something occurring. Use „erscheinend“ when something is beginning to become visible and „auftretend“ for a general statement.

Die erscheinenden roten Flecken wurden nach dem Duschen deutlich sichtbar.
The red spots that appeared became clearly visible after showering.
Die auftretenden Schmerzen verschwinden nach kurzer Zeit wieder.
The pain that occurred disappeared again after a short time.