Your private key is a randomly generated string of letters and numbers that allows you to control and spend your Bitcoin. The private key is always mathematically related to your wallet; however, it is impossible to reverse engineer due to the SHA256 hashing process discussed earlier in this lesson.
Your public key is also mathematically related to your wallet, and however, in this case, the wallet address is a hashed version of your public key. The public key can be derived from the private key, but that process cannot be reversed to obtain the private key.
Stated, your wallet generates both your public key and private key. All three are interrelated through mathematical formulas; however, the private key cannot be obtained by having only the wallet address or public key.