I would argue that having your repository on github is a strong way to say "feel free to contribute". Not saying spam is OK, just that having to ask repo maintainers their authorisation seems superfluous.
How are they different as long as they are not spam? Good contributions are good contributions and help, regardless if there's a crappy t-shirt or not in exchange for them
It's the incentive structure. It's effectively Goodhart's Law in action: When a measure becomes a target, it ceases to be a good measure. In this case, the measure is "number of pull requests", and the result of making it a measure is that people created an insane number of PRs that simply adjusted white space in a README or slightly reworded phrases but kept the exact same meaning. Because they wanted the T shirt, because they felt that it validated them as a developer (ignoring that good contributions would have been a much better validation).
The people who participate are different and pull requests are different.