Yes, I totally agree and so I brought some slides to illustrate
What we think of as a typical compressor is the piston/cylinder design our motors are;
piston goes up, compresses the air/fuel into a smaller volume.
This is called a Positive displacement compressor.
But a Centrifugal compressor is not a positive displacement compressor, it works a little different
these pics are of a machine used to compress vapor refrigerant, it is driven by a large electric motor but the compressor end is quite the same as what we call a turbo charger.
Just imagine a turbo unit about 36-48" across.
the compressor uses three main parts , the impeller, the diffuser, and the volute.
the vapor enters through the center, and then is quickly spun out into the diffuser, which is just sort of a ring with little holes in it, but this slows down the vapor while the impellor is continuously slamming more molecules on top of it.
This is how the vapor is compressed. Then, in the case of a car's turbo system, we now feed Compressed air to the system and you get a lot more Bang out of it.
the 'electric supercharger' is only the impeller without the compressor, so it certainly does not get the same effect.
and if you're running higher pressure you need stronger, larger pipes to manage it.