Since chemistry is the study of all matter, it is an extremely broad field, both in chemistry and in chemical engineering. It has been divided into more-or-less roughly defined subsets based on the types of properties you are interested in, or the sources of materials. Material science is the study mostly of bulk and surface physical or chemical properties of materials. Thinks like strength, flexibility, hardness, density, conductivity, corrosion resistance, and other bulk properties are related to molecular and macromolecular structure of the materials.
Some other subgroups include:
Medicinal chemistry - study of physiological effects of chemicals and the interactions of chemical structures with biological structures.
Biochemistry - study of the reactions of biological systems on a molecular level and the molecular products of biological processes.
Petroleum chemistry - study of materials and reactions of materials found in petroleum
Nuclear chemistry - study of the nucleus and changes and reactions that occur in the nucleus and between nuclei.
Food chemistry - study of materials consumed or designed to be consumed
Polymer chemistry - study of properties, reactions, and production of very large molecules made of smaller repeating subunits
and so on, ad infinitum. A copy of Chemical & Engineering News (if you're an ACS member or know one) will give you an idea of the wide variety of different sub-disciplines which have a large enough population to need separate listings. These sub-disciplines evolve rapidly based on new discoveries and new uses.
Each of these sub-disciplines can have both chemistry and chemical engineering components; in general, the chemistry side looks at small scale interactions and reactions, while the engineering side looks at production scale and manufacturing processes. Hence biochemistry and bioengineering, material science and materials engineering, etc.