Retraction: This is the most common and general term, meaning a formal statement that acknowledges an error in a published story and takes it back.
Correction: This is used for smaller errors, such as factual inaccuracies or typos. It's usually placed prominently in the newspaper, often at the bottom of the original article or in a designated "Corrections" section.
Apology: This goes beyond simply stating a mistake. It expresses regret and sometimes even remorse for the error and its impact. An apology is more likely to be issued when the error is significant or the publication's reputation has been harmed.
Clarification: Used when the original article was factually accurate but misleading, or when additional information needs to be provided to present a complete picture.
Statement of Regret: This is a formal statement expressing regret for an error, but without explicitly retracting the original publication. It may be used when the publication stands by the substance of the article but acknowledges a mistake in its presentation or wording.
Formal Acknowledgement: This term can be used for a simple acknowledgment of an error without a full retraction or apology, especially if the error was minor or unintentional.
The specific term used will depend on the nature of the error, its severity, and the newspaper's editorial judgment.