What is a flag which displays the owner's badge instead of their arms called?

The correct term for a flag that displays the owner's badge instead of their arms is known as a standard. A standard typically functions as a personal flag for individuals or organizations, showcasing an emblem or badge that represents their identity, rather than the broader heraldic arms associated with a family or state.

In contrast, union flags typically refer to flags that incorporate elements of other flags, such as the Union Jack of the United Kingdom, which combines the crosses of St George and St Andrew. A garrison flag is a larger flag flown at military installations, primarily for display purposes, while a storm flag is a smaller, more durable flag used in inclement weather. Understanding these distinctions helps clarify why a standard is specifically associated with personal insignia, distinguishing it from other types of flags that serve different purposes or represent different entities.