Maybe you can post a couple pictures of the engine, etc.
1) The antifreeze (coolant) runs through the engine and the heat exchanger (tank) . . . so the coolant gets hot from running through the engine. . . something must cool it down or it will continue to get hotter.
2) Water is drawn from the lake/ocean (raw water) through the outdrive and up to the heat exchanger (tank). Within the heat exchanger there are many small tubes that run through where the coolant resides, The raw water runs through these small tubes, keeping it separate from the coolant. The coolant and the raw water never meet, but they exchanger heat. So, the hot coolant cools down and the raw water heats up.
3) the raw water, now hot, needs a place to go . . . so it continues along its journey to the exhaust and goes out the Y-tube back into the lake/ocean.
4) the coolant (now cooled) goes back into the engine to grab more heat, making it hot again. . . and the process continues.
As to your specific questions/comments . . .
"I thought that since I have antifreeze in the tank that NO water was exchanged between fresh water and the normal self contained system that is provided by the water pump." No water is exchanged only the heat from the coolant and water are exchanged. The heat from the coolant goes into the water.
"I do not know what a sea water pump is and do not think one is on this engine. " There is a pump either in the outdrive or on the engine. This is in addition to the 're-circulating pump' that is on the front of the engine, similar to what is in a car engine. The sea water pump's job is to bring the lake/sea water up to the engine . . . in this case it brings it to the heat exchanger, as that is where the exchange of heat is taking place.
"I also thought that no water was drawn into the system from the water that the boat sat in and only pushed out exhaust from the engine through the bottom of the Y tube." Where would that water originate from, if it did not come from the lake/ocean?
I hope this further explanation helps. A closed cooling system on a boat engine is essentially 2 cooling systems and sets of plumbing. 1 for the coolant and 1 for the sea water. The heat exchanger is where the coolant transfers its heat to the sea water.