There are several examples of discrete lattice recursions that have been qualified as being somehow integrable and being related to the well-known flows associated to the KP equation on an infinite dimensional Grassmannian. This work aims to clarify the relation, in the general linear (Hirota) and symplectic (Keshaev, Kenyon-Pemantle) cases. The first hint of the link lies in the fact the recursion equations can be thought of as (short) Plücker relations (or their Lagrangian counterparts). These generically imply all Plücker relations, and the recursion flow can be solved in terms of KP tau-functions. This works in the orthogonal case, too. (Joint with Semeon Arthamonov and John Harnad)