"Pooled" and "stratified" are conventional terms in the statistics literature. A pooled estimate is computed using all observations from all groups (classes). A stratified estimate is computed for each group (class) separately.
Every method in CLASSIFY computes the Mahalanobis distance from the center of each class (determined from the training data) and the data in sample. 'mahalanobis' method assigns an observation to the class with the minimal distance. All other methods estimate the posterior probabilities and assign an observation to the class with the largest posterior.
