In terms of Mercruiser, there are 2 types of outdrives which determine the type of pump that draws the water up to the engine.
Alpha drives have the pump in the outdrive.
Bravo drives have no pump in the outdrive, instead have a pump running off of the engine pulleys.
These pumps are separate from the recirculating pump that is on the front of the engine, same as an automotive engine.
the difference between Alpha and Bravo pumps may be what is confusing you. So, with a Bravo there are actually 2 pumps that are run off the engine pulleys, but one of them is really associated with the outdrive
The pump that is associated with the outdrive brings weather to the engine, and by doing so pushes water out of the engine.
The recirculating pump merely sends water around the engine block
So, you have 2 pumping functions going on.
1) drawing water in, which displaces an equal amount of water out
2) recirculating water through the engine.
I hope this helps.