It is basic.
Think of a garden hose with a balloon on one end, you need to inflate the balloon to move an object with is being pushed back from the opposite direction by a spring.
So you blow into the garden hose (boost pressure) the balloon inflates and pushes the object back as it over comes the spring pressure.
now poke a hole in the hose and try to blow it up, you blow the exact same amount of air as the first time, but now because the hose has a hole in it the balloon doesn't inflate as much and doesn't move the object as far because you are loosing pressure through the hole in the hose
Now think of the wastegate being the object you are trying to push, the spring as the spring holding the wastegate shut and the balloon as the diaphragm pushing the spring, and the hose as the vacuum line from the actuator to your intercooler piping.
The excess pressure is simply vented out the hole in the boost controller into the engine bay.
what you are thinking of in part of your post is the blow off or recirculation valve.
What that does is when you close the throttle (let off the loud pedal) all the pressure in the intercooler piping has nowhere to go but back where it came from (back out the turbo) making the "dose" noise or the tu tut tutut utut noise you often here.
Big conjecture as the whether it does any damage to the turbo or not.
So the factories started fitting recirc or blow off valves.
Work similar to a wastegate but backwards, they close up tight under boost and release when the throttle plate is closed.
They too are fed boost, but from the intake manifold only, so they are fed boost to hold the valve closed, plus a spring to hold it closed too and when you back off the throttle because the intake manifold is now under vacuum that same boost feed + the pressure in the intercooler pipes opens the valve to let the excess pressure out, either back into the intake before the turbo (legal) or straight out to atmosphere (not legal) illegal due to the noise plus the air in the intake system is full of oil vapor / fuel vapor etc and might kill some baby seals or some shite.
Also cars fitted with Mass Air Meters (AFM or MAF) like the skyline dont like externally venting blow off valves, because the air flow meter measures the amount of air being sucked in and tells the ECU to add fuel for that amount of air.
Except the engine doesn't receive that air but the computer thinks it does so it throws a whole heap of fuel in thinking all that air is making it into the engine, causes stalling issues and horrid fuel economy.
Where as when plumbed in, you will see it feeds back into the intake between the turbo and the AFM it just gets recirculated back around and reused, so the amount of air the AFM reads is now correct for the amount of air the engine is receiving.
Hope that makes sense, made it as basic as I could