A private key is just a random generated number. This number is then hashed using SHA256.
The private key is NOT being hashed.
The private key is used to calculate the public key through multiplication on the elliptic curve.
This public key is afterwards being SHA-256 hashed and afterwards RIPEMD160 hashed to get the address.
Mining, on the other hand, does rely on double-SHA256-hashing a block with a nonce which does result in a hash below the given target.