Cominuscule flag varieties generalize Grassmannians to other Lie types. Schubert varieties in cominuscule flag varieties are indexed by posets of roots labeled long/short. These labeled posets generalize Young diagrams. In this talk, I will report on joint work with E. Richmond and M. Tarigradschi showing Schubert varieties in potentially different cominuscule flag varieties are isomorphic as varieties if and only if their corresponding labeled posets are isomorphic. Our proof is combinatorial in nature and type-independent. The talk is based on the arxiv preprint available at https://arxiv.org/abs/2302.11642.