That was a different person who replied, but their explanation is correct!
Furthermore, the distinction is much more than just pedantic. Hydrogen production from electrolysis (which theoretically can be carbon neutral) is about 3x as expensive as hydrogen production from steam reformation (which realistically can't be carbon-neutral). And I'll give you one guess which method all the hydrogen articles talk about…
When put in those terms, it becomes quite obvious that the whole operation is a fossil fuel bait-and-switch.