Cold Storage Question (Beginner)

Sorry if this is a dumb question but I'm still trying to understand how cold storage works. I understand that your BTC is stored on the blockchain and not physically in the wallet...

But if you can restore a lost/stolen wallet with the 12 word seed phrase....then does the cold storage wallet (ie. ledger or trezor) just store your seed phrase? Is that all its effectively storing since your crypto is on the blockchain?