The primary difference is that plain rabanut does not have full control over which ingredients they do or did not accept. It is only meant to be a minimal standard of kosher and they all accept from each other. They are all only as good as the weakest link
That is a very accurate description.
Since we are talking minimal standard, and relying on other weak links, there is also less use of Mashgichim at various stages.
IINM the Mehadrin "standard", at least for some "Rabbanut Mehadrin" and even private labels, also accept anything that otherwise says Mehadrin on it, which means it is as strong as that weakest link.
Since the Rabbanut is a governmental agency, they are limited in what they can reject, even in the Mehadrin standards. IINM in Tzfas they have 3 types of certificates for establishments, regular, Mehadrin (as per Rabbanut requirements) and another one for those who are really scrupulous and want something that is up to the local Rabbi's personal standards.