Engineers usually work on projects that have a good chance of success - they typically don't test the boundaries. Researchers, on the other hand, are searching for new knowledge by doing science that has never been done before. Failure comes quite often. But with every failure, new knowledge is obtained. That's what I love about research.
Working at NASA as an undergrad gave me a lot of hands-on experience in both engineering and research. It wasn't until I started working on research in grad school that I realized the difference. It takes a lot of courage to do research as an engineer. It's a complete paradigm shift from what engineering is typically defined as.
I am currently studying in the field of Additive Manufacturing (AM) (aka 3D Printing) in the DREAMS Lab (Design, Research, and Education for Additive Manufacturing) at Virginia Tech. I can't imagine a more exciting field. In my lab, I've had the opportunity to operate, repair, and explore the working principles behind many different types of AM machines. The links below contain my work in the DREAMS Lab as well as other research I have participated in at NASA.
Homer Hickam and me at NASA MSFC