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.
What about "my private key is generated from 111th block's hash in bitcoin blockchain"? You do not remember exact value which is used to produce private key, but you remember the way how to find it - exactly like "my phrase is second verse of song X".
One thing is sure in my opinion - brain wallets belongs to past.