The way I understand it, the private key and the public key have a special “asymmetric” relationship.
The public key is derived from the private key and you can derive many public keys “easily” and quickly and these public keys can easily be proven to belong to the holder of the secret private key that generated it or signed a particular transaction.
The private key on the other hand cannot be “easily” derived from the public key and therein lies the power of the public key cryptography or as it’s often called, “asymmetric” cryptography.
That relationship between public and private keys within the context of Bitcoin and other cryptocurrencies is their power, but individually.
The public and private keys are just numbers. Very large Integers. That’s all.
I could guess a very large number … 102389328309242483089283092 … and that might be the private key of a Bitcoin wallet that holds, 1000 Bitcoin. It took no effort on my part to propose that it might.
If I’m wrong, guessing the next 5000 Trillion numbers might take a while and I’m tired.