Current deep learning models often achieve excellent results on benchmark image-to-text datasets but fail to generate texts that are useful in practice. We argue that to close this gap, it is vital to distinguish descriptions from captions based on their distinct communicative roles. Descriptions focus on visual features and are meant to replace an image (often to increase accessibility), whereas captions appear alongside an image to supply additional information. To motivate this distinction and help people put it into practice, we introduce the publicly available Wikipedia-based dataset Concadia consisting of 96,918 images with corresponding English-language descriptions, captions, and surrounding context. Using insights from Concadia, models trained on it, and a preregistered human-subjects experiment with human- and model-generated texts, we characterize the commonalities and differences between descriptions and captions. In addition, we show that, for generating both descriptions and captions, it is useful to augment image-to-text models with representations of the textual context in which the image appeared.