I thought the mini private key format, used for Casascius physical bitcoins should rate a mention here, because it's basically a SHA256 brainwallet... but with a randomly generated passphrase.
...
...
The private key is simply the SHA256 hash of the string, like a brainwallet.
The fact that the private key is derived using SHA-256 does not make it a brain wallet. A HD wallet seed comes from the SHA-512 hash of the BIP-39 seed phrase. Does that make an HD wallet a brain wallet?
A brain wallet is derived from something that can be memorized. That is why it is called a "brain" wallet. The mini-key is a random sequence and is not intended to be memorized so it is not basically a SHA-256 brain wallet.