  Leclerc constructed a conjectural cluster structure on Richardson varieties
in simply laced types using cluster categories. We show that in type A, his
conjectural cluster structure is in fact a cluster structure. We do this by
comparing Leclerc's construction with another cluster structure on type A
Richardson varieties due to Ingermanson. Ingermanson's construction uses the
combinatorics of wiring diagrams and the Deodhar stratification. Though the two
cluster structures are defined very differently, we show that the quivers
coincide and clusters are related by the twist map for Richardson varieties,
recently defined by Galashin--Lam.
