I have a number of NANO boards which, as it turns out, have the 328PB soldered on them.
The -PB versions have extra functionality over the standard -P version.
2 functions come through the procesor pins 3 and 6: SDA1 and SCL1, for an extra I2C bus.
In the -P version these pins were: 3=GND and 6=VCC
I noticed that on the boards with the -PB processor these pins are
still connected to the power lines GND and VCC
Apart from the fact that these processor pins are not externally
connected to 2 additional pins and therefore useless, they might even get damaged. I think...
But if you don't, it should be OK. The pins are on PORTE, which doesn't exist on the normal P version, so you'd have to go to some effort to make them outputs.
I have no reason to believe that the chip is genuine or not.
Years ago I bought a few nano's for some experiments
Some boards had the 328P and some boards had the 328PB on it.
So I think that what westfw writes could be true: cheaper and more available.