Those hardware wallets still require a wallet on a connected computer in order to function. They can interface with certain wallets, you will need to check their websites to find out which ones. Those wallets create the transaction and then sends it to the hardware wallet for you to authorize it to sign the transaction. Then the transaction is sent back to your computer and broadcast through your computer.

The hardware wallets generate the addresses. The addresses are generated deterministically from a seed, meaning that the same algorithm is always used and when using the same seed, the same set of addresses are produced. The recovery words are just a representation of that seed.