Biomedical engineering is one of the newer fields of engineering, first recognized as a discipline back in th elate 1940s. It's origins, however, date back to the first artificial limbs made of wood and other materials.
Biological engineering is on of the newer fields of engineering that spans the fields of biology and engineering. It applies concepts from mathematics and physical sciences to design, analyze, and manufacture inanimate products and processes to address human and environmental needs.
Chemical engineering differs from most of the other fields of engineering in its emphasis on chemistry and chemical nature of products and processes.