plsda — PLS discriminant analysis (PLS-DA) with cross-validation: a PLS2 (Simpls) computes scores from the disjonctive matrix of the classes, then each observation is attributed to a class using these scores
plsfda — PLS factoriel discriminant analysis (PLS-FDA) with cross-validation: a PLS2 (Simpls) computes scores from the disjonctive matrix of the classes, then a factoriel discriminant analysis is applied to the scores, yielding new scores; each observation is attributed to a class using these new scores