A basic fume hood is designed to protect the laboratory workers from chemical fumes. Room air is brought into the fume hood and exhausted through duct work to the outside. Negative pressure is maintained in the laboratory so that the workers are not exposed to the fumes generated in the hood. A fume hood is not designed to handle potential biohazards or particulates.
A biological safety cabinet is designed to protect the scientist and other members of the laboratory from possible biological hazards. The biological safety cabinet brings room air into the cabinet creating a negative pressure so that any biological agents remain in the hood. The air in the cabinet is passed through a HEPA filter and either vented back into the laboratory or vented to the outside. The HEPA filter traps the biological agents. The filter must be periodically changed and is treated as a biohazard. If the biosafety cabinet is totally vented to the outside small amounts of volatile chemicals may be used in the cabinet.
Both of these safety cabinets are designed to protect the worker from the work, they do not protect the work from contamination.