What is the difference between SVM Rank and SVR (Support Vector Regression)?

One is used for ranking and the other is used for regression.

There is a crucial difference between regression and ranking. In regression, the absolute value is crucial. A real number is predicted.

In ranking, the only thing of concern is the ordering of a set of examples. We only want to know which example has the highest rank, which one has the second-highest, and so on. From the data, we only know that example 1 should be ranked higher than example 2, which in turn should be ranked higher than example 3, and so on. We do not know by how much example 1 is ranked higher than example 2, or whether this difference is bigger than the difference between examples 2 and 3.