Definition of "Bio & Engineering" terms from the MIT Biological Engineering Division:
Bioengineering (BioE) -- an APPLIED FIELD of engineering in biological materials and systems.
Biomedical Engineering (BME) -- an APPLIED FIELD of engineering in medicine and biomedicine, generally inter-disciplinary in nature.
Biological Engineering (BE) -- a new engineering DISCIPLINE grounded in biology, particularly mechanistic biology at the molecular and cellular levels, with novel applications to biomedicine as well as biotechnology; it also enables new approaches to fundamental discoveries in bioscience.
BE vs. BME at MIT -- The crucial distinction is that Biological Engineering (BE) is a new engineering discipline, distinguished by having biology (particularly molecular cell biology) as its foundation science, just as how Mechanical Engineering and Chemical Engineering, for example, have theirs in physics and chemistry. Biomedical Engineering (BME) and Bioengineering (BioE), on the other hand, are application fields for any engineering disciplines. This is why MIT will be offering a MAJOR in BE, but only a MINOR in BME for students majoring in other departmental disciplines.