Containment and support have traditionally been assumed to represent universal conceptual foundations for spatial terms. This assumption can be challenged, however: English in and on are applied across a surprisingly broad range of exemplars, and comparable terms in other languages show significant variation in their application. We propose that the broad domains of both containment and support have internal structure that reflects different subtypes, that this structure is reflected in basic spatial term usage across languages, and that it constrains children's spatial term learning. Using a newly developed battery, we asked how adults and 4‐year‐old children speaking English or Greek distribute basic spatial terms across subtypes of containment and support. We found that containment showed similar distributions of basic terms across subtypes among all groups while support showed such similarity only among adults, with striking differences between children learning English versus Greek. We conclude that the two domains differ considerably in the learning problems they present, and that learning in and on is remarkably complex. Together, our results point to the need for a more nuanced view of spatial term learning.