Clonally propagated crops exhibit great diversity and are integral components of global and regional food systems. At the same time, little is known about the mechanisms that generate diversity within clonal crop species, and this diversity is increasingly threatened by economic, environmental, and social change. Research addressing the genetic basis for folk classification of clonal crops can address both of these challenges. Here, we carry out such research through a case study of the Andean tuber crop, oca (Oxalis tuberosa Molina). We employ ethnobotanical and molecular genetic methods to assess the congruence in partitioning of 216 oca accessions with respect to 26 folk taxa and with respect to 31 genetic clones. We find that the greatest number of folk taxa (11) correspond to single, unique genetic clones, but we also identify two instances of single folk taxa comprising multiple genetic clones and two instances of multiple folk taxa comprising single, shared genetic clones. We discuss the potential roles of different diversity-generating mechanisms, such as somaclonal variation and sexual reproduction, underlying these varied forms of congruence in order to inspire more directed research on this topic. We also discuss the implications of our findings on in situ and ex situ conservation work, in which practitioners often approximate crop genetic diversity by counting folk taxa. Ultimately, we argue that efforts to understand and conserve clonal crop diversity will be most effective when both folk classification and its genetic basis are considered together.