Linear regression and linear discriminant analysis are very different. Linear regression relates a dependent variable to a set of independent predictor variables. The idea is to find a function linear in the parameters that best fits the data. It does not even have to be linear in the covariates. Linear discriminant analysis on the other hand is a procedure for classifying objects into categories. For the two-class problem it seeks to find the best separating hyperplane for dividing the groups into two catgories. Here best means that it minimizes a loss function that is a linear combination of the error rates. For three or more groups it finds the best set of hyperplanes (k-1 for the k class problem). In discriminant analysis the hypoerplanes are linear in the feature variables.
The main similarity between the two is term linear in the titles.
