Continual Learning (CL) and Streaming Machine Learning (SML) study the ability of agents to learn from a stream of non-stationary data. Despite sharing some similarities, they address different and complementary challenges. While SML focuses on rapid adaptation after changes (concept drifts), CL aims to retain past knowledge when learning new tasks. After a brief introduction to CL and SML, we discuss Streaming Continual Learning (SCL), an emerging paradigm providing a unifying solution to real-world problems, which may require both SML and CL abilities. We claim that SCL can i) connect the CL and SML communities, motivating their work towards the same goal, and ii) foster the design of hybrid approaches that can quickly adapt to new information (as in SML) without forgetting previous knowledge (as in CL). We conclude the paper with a motivating example and a set of experiments, highlighting the need for SCL by showing how CL and SML alone struggle in achieving rapid adaptation and knowledge retention.