It is two names for the same thing. Both are methods that retrieve pattern highly frequent in one class while not frequent in other classes.
For more information on such patterns, you can have a look at Characterizing Discriminative Patterns.
If you are not looking for speed, you can use a standard sequential pattern mining algorithm and just compute a measure comparing the frequency of the computed sequential patterns in each class. The patterns having the highest value are then the emerging (or discriminative) patterns. This method allows to test several approaches and is very easy to implement.
If you are interested in performance, then the idea is to avoid exploring some part of the search space where you know that you will not be able to find any emerging pattern above a given threshold. Such algorithm may be much more efficient, but are highly dependent on your measure to discriminate pattern.