Probably the difference is that Biochemistry is in the Chem Dept and Chemical Biology is in the Biology Dept. Which department interests you more? Look on college websites about future job posibilities.
Jobs directly related to your degree include:
Analytical chemist.
Biomedical scientist.
Healthcare scientist, clinical biochemistry.
Clinical research associate.
Forensic scientist.
Physician associate.
Research scientist (life sciences)
Scientific laboratory technician.