The difference is that Bitcoin is designed to be "just" an append-only* timestamped linked list, with some rules on how a new node can look like in order to be successfully appended. Making the creation of a canonical linked list possible between hostile actors is the whole innovation. The currency stuff is "just" a cool practical application tacked on the linked list
LLMs by contrast are not designed to just repeat what's already in the instructions, no matter which stance on LLM design you subscribe to
* exceptions apply