Yes.

But...

If they are just offline (in terms of internet connection) calculators, how do the keys and seed phrase get generated and then used online to correctly approve transaction? I am not seeing how those two things work.

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keys are generated offline in a one way process. you can for example install Electrum on a PC without internet and create a whole set of new keys. An address generated offline is then unknown to the blockchain until you transact with it. This also means that you can sign a transaction on an offline device to then broadcast it from an online device. The tx is already signed and cannot be tampered with.