I don't think people even know what they mean when they talk about startup ideas generally.

If the Bitcoin paper is an implementation, then what is the idea? You could argue that the "idea" would be something like "a distributed trustless transaction protocol" or something.

But then you could as easily argue that that's not an idea. That's a goal.

Inversely, you could argue that the Bitcoin paper is not an implementation, that the implementation is the actual software that... implements the content of the paper.

The problem with "idea" and "implementation" is that they're relative concepts that can be used to separate arbitrary parts of complex systems into two buckets, but where that separation doesn't always provide any insight.

Is general relativity an idea or an implementation (of the idea "a better theory of gravitation than Newtonian mechanics")? Is a winning trading strategy an idea or an implementation (of the idea "something that makes money on the stock market")? Etc.

The whole concept of a "startup idea" itself is fraught with imprecisions. Not to mention the assumption that startups are to be based on one singular idea, which is highly debatable.