Very little. The pressure in the pump is allowed to travel through whatever network of pipes it is attached to; the compressor's outflow is just stored in a sealed container.
A centrifugal pump will typically give you a higher flow rate but a lower pressure, where a piston pump will give you more pressure but a lower flow rate.
Pumps -- Centrifugal vs. Positive Displacemen
Two Categories -- Kinetic (Centrifugal) and Positive Displacement
There are two main categories of pumps - kinetic and positive displacement. Almost...