Single progenitors can give rise to any and all of the main retinal cell types: photoreceptors, interneurons (horizontal, bipolar, and amacrine cells), retinal ganglion cells (RGCs), and glia. Many of these types are divisible into multiple functionally, structurally, and molecularly distinct subtypes (e.g., ~25 for RGCs). It remains unknown when and how progenitors become committed to generate such subtypes. Here, we determine the origin of RGCs that respond selectively to vertical motion and express cadherin 6 (cdh6). Using Cre recombinase-based lineage tracing, we show that these RGCs arise from progenitors that themselves express cdh6. These progenitors are capable of generating all major retinal cell types, but the RGCs they generate are predominantly of the single direction-selective subtype. In contrast, cdh6-positive progenitors retain the ability to generate multiple subtypes of amacrine and bipolar cells. Our results demonstrate that type and subtype specification are regulated in different ways and suggest that multipotential but fate-restricted progenitors contribute to subtype specification in retina.