You are right, and "decentralized" would be the proper word. Thats why it is often associated with Bitcoin (and yes, because there are extensions that allow you to "zap" - i.e. attach bitcoin via lightning network to messages. These are optional extensions however, and Nostr serves its own right outside of crypto. In the times of internet censorship and social media ID verification, Nostr is a welcome technology.
Lightning network is a vaporware scam that has never and will never work. It's purpose was to convince idiots that Bitcoin hadn't been taken over when it actually had been by the private company, Blockstream.