The difference between private key and seed phrase is that a private key is a long number that any wallet owner must have to make purchases from their crypto wallet. Private keys are generated with your seed in combination with a key index and are required to sign the transaction.
The seed phrase is given to you when you create a crypto wallet (usually 12-25 words) and used to recover the wallet if you lose access to it. (eg. house fire, hard drive fails, hardware wallet fails, etc)
The seed phrase is a string of 12-25 words that you should stamp using a Safe Seed metal wallet.