Class I:- A cabinet with a front aperture through which the operator can carry out manipulations inside the cabinet. This type of cabinet is suitable for carrying out work on all except hazard group (HG) 4 pathogens. Most potentially airborne particles will be contained within the cabinet. The cabinet must exhaust through a high efficiency particulate absorption (HEPA) filter to the outside air or to the laboratory air extract system if used for handling samples that may contain HG 2 or 3 pathogens. This type of cabinet does not provide any protection of the work.

Class II:- These are deigned to control airborne contamination of the work while at the same time controlling exposure of the operator. An inward airflow passed through a HEPA filter before circulation controls the escape of aerosols and the filtered down flow air passes over the work. Part of this airflow is exhausted to atmosphere through a HEPA filter and make-up air is drawn in through the front aperture. Modern Class II cabinets can provide operator protection of the same order as Class I cabinets but are more susceptible to disturbances of airflows. Class II cabinets should only be used where protection of the work is essential.

Class II Type A (A1/A2):- The Class II Type A biological safety cabinet is the most common Class II cabinet. It is also the most common safety cabinet of all the different types available. It has a common plenum from which 30% of air is exhausted, and 70% re-circulated to the work area as the downflow. Type A cabinets exhaust air directly back to the laboratory, and they may contain positive pressure contaminated plenums. When toxic chemicals must be employed as an adjunct to
microbiological processes, these cabinets should not be used. Exhaust HEPA filtration only removes airborne aerosols including biohazards, and not chemical fumes. The Class II Type A1 has the positively-pressurized contaminated plenum bordering the ambient environment, and therefore is less safe than the Class II Type A2 that has a negative pressure surrounding the positively pressurized contaminated plenum. In case there is a leakage on the positive plenum, the leaking aerosol will be pulled by the negative pressure back to the positive plenum, and it will not leak out. Because of the safety issue, the Type A1 design is now considered obsolete. In the A2 cabinet, about 70% of air from the positive plenum is recirculated as downflow, and the remaining 30% is discharged to the lab through the exhaust filter.

Class II Type B:- The main difference between Type A and Type B cabinet is: Type B cabinets must be operated with an external blower and it exhausts air to the external environment via a dedicated ductwork system. Without the external blower, the cabinets internal blower will blow the
air (and microbiological agents) inside the work zone through the front opening, towards the operators’ face, creating a dangerous situation. This cabinet is not self-balancing, in the sense that its own blower can only create downflow, and the cabinet relies on the external blower to create inflow.
On all Type B cabinets, environmental protection may be enhanced by installing a scrubbing system between the exhaust of the cabinet and the final exhaust point outside the building to neutralize the chemical fumes present in exhaust air. Although Type B cabinets are commonly used when chemicals are involved in your work processes, they theoretically provide an increased level of safety as compared to other Type A cabinets. By exhausting air directly to the external environment, they provide an additional “fail-safe” in the event that the regular exhaust HEPA filtration ceases to function.

Class II Type B1:- The Class II Type B1 biological safety cabinet was originally specified by the American National Cancer Institute. It has a common plenum from which 70% of air is exhausted, and 30% re-circulated to the work area as the downflow. Type B1 cabinets also have a dedicated exhaust feature that eliminates re-circulation when work is performed towards the back within the interior of the cabinet. Toxic chemicals employed as an adjunct to microbiological processes should only be employed if they do not interfere with work when re-circulated in the downflow.
 
Class II Type B2:- In the Class II Type B2 cabinet all inflow and downflow air is exhausted after HEPA filtration to the external environment without recirculation within the cabinet. Type B2 cabinets are suitable for work with toxic chemicals employed as an adjunct to microbiological processes under all circumstances since no re-circulation occurs. In theory, Type B2 cabinets may be considered to be the safest of all Class II biological safety cabinets since the total exhaust feature acts as a fail-safe in the event that the downflow and / or exhaust HEPA filtration systems cease to function normally. However, Class II Type B2 cabinets are, in practice, difficult to install, balance and maintain.
 
Class III:- These are totally enclosed cabinets. The escape of airborne particles is prevented by a HEPA-filtered exhaust. A HEPA inlet filter supplies sterile air to the interior. Because of the airflow pattern there is a greater risk of contamination of the work following a spill than in a Class I cabinet. Class III cabinets are primarily designed for total containment of HG 4 pathogens although their use is advised for work with high titre cultures of some HG 3 pathogens.

Class I/III Hybrids: – These are Class I cabinets that are said to be modifiable to Class III. Prospective purchasers must be aware that these must be retested to demonstrate satisfactory operator protection in the Class III mode.
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Reference links
http://www.escoglobal.com/resources/pdf/biosafety-booklet.pdf
https://www.bakerco.com/introduction-biological-safety-cabinets