There are typically two basic types of breast pumps:
Closed-system pump or clinic grade breast pump: Also called "flood security," a closed-system pump is one that is closed from the milk by an object. This is the most hygienic kind of pump, as the object keeps milk from getting into the machine, which can make cylinders and little pieces difficult to clean. They are more expensive.
Open-system pump: These don't have any object between the milk and the pump instrument, so milk flows through cylinders and other little pieces into the bottle and also interacts with the pumping component. Open-system pumps are generally more affordable than closed-system pumps.