An Aspirator a device based on the "Venturi Effect" in which a moving fluid (H2O) in a tube with a smaller diameter is inserted a very short distance into a tube of a larger diameter (Aspirator). [See http://www.coleopsoc.org/scarabs/scarabs_9.pdf (http://www.coleopsoc.org/scarabs/scarabs_9.pdf)
] The moving water when you turn on the faucet will suck air, i.e. create a vacuum.
A water pump could be one of many things, but typically is a device powered by an electric motor that turns an impeller (turning fan-like water wheel) that "scoops" the water through an intake port and out the discharge port.
The two can be combined quite effectively (A high speed water pump like a Sump pump with an Aspirator) to create an excellent quality vacuum device. (Mine pulls almost 29") You can make it "self contained" ; i.e. in a 5 gallon bucket and the water gets re-circulated over and over. Adding ice to the water will increase the strength of the vacuum.
Rhodiums Web site has an example of this: https://www.thevespiary.org/rhodium/Rhodium/chemistry/equipment/aspirator.html (https://www.thevespiary.org/rhodium/Rhodium/chemistry/equipment/aspirator.html)
If they drive God from the earth, we shall shelter Him underground - Dostoevsky