It's not a booster, as I've already said. It's a third dose. Boosters are given after six months, primary doses twelve weeks apart. Those eligible for third primary doses will get a booster six months after their third dose.
No one has any idea whether it's a booster or a third dose. Anyone who claims otherwise is lying, and if you believe them, you've been lied to.
The distinction is that if it's really a third-and-final dose rather than a booster, no additional doses would be necessary for quite some time afterward - much longer than six months. But no one has any idea whether that's true or not, just like they didn't have any idea whether a third dose would be necessary after the first two. That didn't stop anyone from telling people it wouldn't be. Maybe immunity will last 10+ years after the third dose, or maybe people will need another dose in a few months. Which those same people will undoubtedly insist is a "fourth dose" rather than a "booster." Maybe by the time we get up to nine or ten "initial doses," people will be more willing to question these evidence-free assertions about how long the protection lasts.
The only reason they're calling it a "third dose" rather than a "booster" now is because many global relief organizations have understandably criticized administering booster doses when most of the world still doesn't have access to the initial doses. I'm not sure why calling it something else would change anything there, but I guess that's why I'm not in charge of PR.