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A Hierarchical Deterministic wallet, introduced through BIPs 32 and 44, also generates multiple keys from a single private key, like the Deterministic wallet stated above. The difference is that each one of those keys can further generate their own subset of keys and so on so forth. Essentially, you have a master or parent key, which can then generate child keys, and they can then generate grandchild seeds.
Throughout all these different wallets, we are still dealing with really long strings of letters and numbers that are difficult for humans to retain and process. Then comes along BIP-39, a proposal which offers as a solution a way to convert those long strings of binary or hexadecimal digits into something that is much easier for humans to read and transport. This is the most popular implementation for private keys and most of you have probably already interacted with it.
Implementing a passphrase varies from wallet to wallet. Doing it on the Coldcard is quite simple. You even have the option of adding words from the BIP-39 word list directly instead of adding individual characters. Take a look at the guide here!