|MadSci Network: Engineering|
Good question. In general, people in both of these fields work on improving or analyzing the performance of materials by investigating their atomic or molecular structure or how the materials interact with the environment around them. Let's break your question down and look at metallurgical engineering and materials engineering separately.
Metallurgical Engineering is specifically involved with engineering metals. A Metallurgical Engineer might be involved in failure analysis investigations (like the material analysis done on the Titanic), or they might be involved in designing new metals (like Liquidmetal), improving processing methods (new metal forming or joining techniques), or improving properties of existing metals. They may work in an office, or they may work in a manufacturing facility that casts thousands of gallons of molten metal at a time.
Materials Engineering is a much broader field that covers not just metals, but also non-metallic materials, like ceramics, polymers, and composites. These days, micro- and nano-scale devices are often designed with the help of Materials Engineers, who understand the characteristics of materials on an atomic scale. The Minerals, Metals, and Materials Society (TMS) has a great website that gives more information about Materials Engineering. If you follow their link to MSE People, you'll find 25-30 different career profiles related to Materials Engineering (some are actually Metallurgical Engineers). ASM International also provides some information on careers for Materials Engineers here.
I hope this information helps you find a field that is interesting to you!
Try the links in the MadSci Library for more information on Engineering.