We document the history of terms used to describe Heinrich (H-) layers and events and which mark major glaciological iceberg discharge events in the North Atlantic. We argue that the usage “Heinrich layer,” “Heinrich zone”, or “Heinrich event” should be restricted to only those sediments that can be ascribed to an origin from the Hudson Strait Ice Stream and the Laurentide Ice Sheet. We also argue that the commonplace understanding of these events---as dominated by massive iceberg discharges ---fails to include the earlier well-documented evidence that these events were also massive meltwater events linked to deposition along the North Atlantic Mid-Ocean Channel (NAMOC) in the Labrador Sea. We make five recommendations for future usage of “Heinrich events,” which include: restricting the usage to those events that can be mineralogically/geochemically linked to Hudson Strait; abandoning the term “Heinrich stadial”; and promote local terminology for “ice rafted events” that may be correlated, or not, with Hudson Strait Heinrich events based on calibrated radiocarbon dates or other appropriate chronological markers.