A private key is a secret password that is unique that controls a public key inside a blockchain.
The public key is named "public" because it is visible to anyone on the blockchain.
The private key is named "private" because it must be kept secret and secure as it is the only way to control the public key.
The private and public keys are associated because the public key is created by passing the private key through a cryptographic mathematical function.
In this way they are inherently connected and are usually called a "private and public key pair".
If you have a private key in clear text, this format is usually called "raw private key".