How is the training for MS students different from MBA students?
An important aspect of MBA training that I haven't seen mentioned in other answers is networking.  A huge amount of getting things done is business is about networking, and while you will not find a formal course on networking in an MBA program, most good MBA programs will have a lot of networking events and opportunities connected with them.  MBA students are also often grouped together in cohorts or otherwise treated much more as a unified group of students than MS students.  All of this adds up to a very important extra-curricular curriculum component that is often a key differentiator for success or failure after business school, and is largely neglected in the more technically focused track of MS students.