Where is seed in Bitcoin Core in comparison to Bread Wallet
In Bread i have to write down my seed and in Bitcon Core i have to backup both passphrase and wallet file. is this true?


Yes.


  Each software has its own seed to private key mechanism. Is this true? 


No. What you call the "seed" is actually called the mnemonic. Most wallets that give you a mnemonic use BIP 39. BIP 39 specifies how the mnemonic should be created and how to convert the mnemonic to an actual seed value.  Most HD wallets then use BIP 32 to convert that seed into your private keys

Bitcoin Core implements BIP 32, but not BIP 39.