Wastegate is in the exhaust tract, allowing exhaust gasses to escape thru the tailpipe without passing thru the turbine side of the turbocharger, as the wastegate only opens when max pre-determined boost is already reached. Any more exhaust would simply drive boost levels too high, theus the use of a wastegate to bleed off excess exhaust.
Blowoff Valve is used to bleed off intake pressure between the compressor side of the turbo or supercharger, and a closed throttle plate (closed throttle between shifts, or sudden letting off of the throttle for sudden deceleration). The closed throttle will not allow the boosted intake charge to be ingested by the engine, so it piles up in the intercooler tubing and intercooler, and once those are full, the boost will run back thru the turbo/supercharger's compressor wheel that could be spinning at upwards of 150,000 rpm or more, potentially stalling it, and causing thrust bearing damage. The cool PSSSSHHHT sound of the blowoff valve that people are hearing has simply been vented to atmoshpere for fun and noise, whereas in OEM applications, the blowoff valve's venting is run back into the airbox or intake plumbing before the turbocharger/supercharger's compressor inlet.
VAriable vane turbochargers like VW's and Porsche's design were first successfully implemented in a production car way back in 1989 by Garrett, Caroll Shelby and Chrysler in the Shelby CSX.........taking the normally aspirated 80 hp 2.2 Dodge 4 cyl, 8 valve, non-cross flow headed K-car engine into the 200hp, and well over 200 ft lbs of torque territory with zero discernible turbo lag. It was an awesome feat back in 89, and that car is still one of my favourites of all time, with it's fibreglass Shelby engineered wheels and Koni full suspension, it was a fantastic little sleeper.
For simplicity's sake, picture the round tunnel doorways on Star Trek type spacecraft that have triangular plates that swirl and converge into the middle to close the door, and swirl out and away from the centre into the walls to open-this is similar to the way the vanes inside the turbine work in this system, constantly changing the volume inside the turbine housing allowing less or more exhaust thru, as well as helping the turbine wheel quickly spool up by staying closed until desired boost is reached.