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.
Using a private key that is derived from in a similar manner is very risky, and is very likely to result in tears. There are many people who are monitoring a large scope of potential addresses for transactions being sent to them, and some of these people look to bitcoin-related forums to increase the scope of these addresses. You can call it a brain wallet if you want, but my advice is to not do it.