So the difference is psycopg2-binary* bundles the libpq native code and pg-native doesn't? I'm no expert, but I think npm packages can include native code if they want thanks to node-gyp, only the node-libpq (which pg-native relies on) author seemingly decided not to package in libpq itself.
* Back when I used this, there was just psycopg2 which had the bin included.