Discrimination = if there are only two groups you can classify based on the discriminant function, if above 0 they are in one group and if below 0 they are in the other. Coefficients of this discriminant function are called discriminant function coefficients.
Classification = when there are more than two groups use the classification functions (the highest clas.function is winner => object is classified into related group). Coefficients of thes classification functions are called classification function coefficients.
Formally it is very simmilar. We could are say that discriminantion is a special case of classification if we have only 2 groups. Discriminant (or discriminantion) function is then a difference of 2 classification functions.