Deltas and fluvial fans are two fan-shaped landforms with complex channel networks. Deltas always occur where rivers enter a standing body of water, such as lakes or oceans. Fluvial fans are inland terrestrial landforms that may form thousands of kilometers from shorelines. Fluvial fans may however also reach lakes and oceans. The current state of knowledge lacks understanding of their morphometric differences or recognition criteria, despite their socioeconomic significance, vulnerability to natural hazards, and important differences in how these landforms respond to global climate change. Moreover, numerous fan-shaped landforms with channel networks have been identified on other planetary bodies, such as Mars and the Saturn's moon Titan, where deltas are important indicators of paleo-shorelines and offer attractive targets for mission sites due to their habitability and high biosignature preservation potential. Here we review the known morphometrics of delta and fluvial fan channel networks, and the differences in their formative processes, and develop morphometric criteria for distinguishing deltas and fluvial fans. We present an ensemble of quantitative metrics that distinguish deltas and fluvial fans and test these criteria on 80 modern channel networks on Earth. Our results improve mechanistic understanding of the fluvial record and delta evolution, provide criteria for accurate recognition of these landforms on planetary bodies and in the sedimentary record, and explain differences in their vulnerabilities to global change.