Fisher’s Linear Discriminant is for classification while Linear Discriminant Analysis is for dimension reduction. How is Fisher’s Linear Discriminant used for classification? The idea is very simple. It first reduces the dimension to one dimensional space using Linear Discriminant Analysis and then  choose average of the two projected means as a threshold  for classification. Therefore, the code is very simple to implement. See pages 13-18 of the slides "Linear Classification" of my computer for details. 
The differences between them have been mentioned by Professor Tao.

Other reference: "Introduction to Machine Learning-dietterich" of my computer