Conversely, you can pay someone a salary and give them less stock than they should really have as a cofounder, and they might still be a cofounder.
As you said, it's to do with the impact that the person has on the business from inception onwards.
So what do you call someone who joins a company before any salaried employees and has equity comparable to that of the founders?
If they don't have any input into the direction the company takes, I'd say that "fools" is a reasonable thing to call them.
Isn't that a separate issue? You can be part of a company from day one and not have any input into its direction, and maybe sometimes you can join late and have significant influence on future decisions.