If you're getting paid, you do need to be getting paid because of some responsibility you're discharging, after all.
You can tell it's two different "ownerships" by what happens if you quit. One you retain, the other is simply redistributed to some other developer. They're not the same thing.
This is English. Multiple definitions for a word are common. Cases where only some definitions apply and not others are common. They happen in almost every sentence. Try to avoid letting that pollute your thought. (It is a challenge. No sarcasm.)
Ownership Leaders are owners. They think long term and don’t sacrifice long-term value for short-term results. They act on behalf of the entire company, beyond just their own team. They never say “that’s not my job."
Unfortunately, we no longer live in a society where the employer-employee relationship is one of trust. The definition Amazon.com seems to be using is that owners do shit work and so should you, but maybe I'm misreading.
Of course, it also has a history of association with servants of landed gentry, which might make people uncomfortable (for good reasons, to the extent the analogy holds up).
"Ownership" is a poor way to express the differences in meaning(s) indicated in this article.