MS&E occupies a slightly odd space in the STEM spectrum, typically associating itself with both science and engineering. So what is the difference between the two, and how does MS&E encompass both?
Science asks why: at a fundamental level, why do materials behave in specific ways? Why is diamond harder than graphite? Science often asks questions for the sake of knowing the answer. There may not be an immediately useful application for something, but that's not the real point of science.
Engineering asks what, when and how: what should I use to build this, when will it fail, and how to I maximize the usefulness of my widget? Engineering takes science and uses it to make and improve things. In the absence of a fundamental explanation, though, engineering makes an empirical model and tweaks it until it is "good enough".
Materials science and engineering departments typically cover a spectrum between "pure science" (e.g., theoreticians) and "pure engineering" (e.g. process development ). But most of what we do lands somewhere in the middle. Quantum studies of structures are often done in line with an experimental group developing fuel cells, or synthesizing organic electronic materials, or studying failure in composites. Creep studies tie back to fundamental diffusion theories from statistical mechanics.
Of course, there's another, more pragmatic reason for the "and engineering". Materials scientists involved in failure analysis projects often get their PE certification to testify as expert witnesses. For many B.S. students, their ultimate jobs will have titles like "Quality Engineer" or "Production Engineer", working on the factory floor. And there's also the idea of ABET certification. There's no clear process of accreditation of science departments, to the best of my knowledge. Being able to say you have an accredited degree opens up international opportunities, and gives departments a way to quickly convey to prospective undergraduates that they will receive a solid education.
Realistically, at the post-bachelor level, all engineering drifts towards the "why" type of questions. Without those questions and answers, we're left with trial and error as a mean of improving our systems. There is certainly something to be said for just doing something, and seeing what happens. On the other hand, being able to make predictions from fundamental knowledge can save time and money in development. Materials science is just a bit more explicit about the union.