The traditions descending from Nichiren are numerous and do not agree, and the twentieth-century history is unusually well documented because much of it happened in public.
Nichiren Shu and the older temple lineages represent one line of descent. Nichiren Shoshu represents another, holding a distinctive doctrine of Nichiren's own status and possessing an object of veneration it regards as inscribed by him. Soka Gakkai, founded in 1930 as a lay educational society, became after the war the most numerically successful new religious movement in Japan, growing through an aggressive conversion practice and building a political party that has been in national government.
In 1991 Nichiren Shoshu excommunicated Soka Gakkai. The dispute was about priestly authority, and it separated a lay organisation of millions from the priesthood it had been affiliated to, leaving both to claim the founder. The mutual polemic since has been sustained and public.
For anyone encountering the practice outside Japan, the practical consequence is that the formula is most often met through SGI, the international arm, whose presentation of it emphasises human revitalisation, peace and individual capability, and which does not present itself in the exclusivist terms Nichiren used. Whether that presentation is a legitimate development or a departure is precisely what the competing lineages argue about.
The formula itself is identical in all of them. What differs is what is claimed about who may authorise its recitation, and about what the object of veneration in front of the reciter is.