The sspx became to be called the new-sspx due to +Fellay's gradual shift towards new-rome, which began with the papacy of Pope Benedict, (who has publicly admitted) that one of his main goals was to get the new-sspx to "make a deal" and become an Indult community (i.e. accepting of V2 and the new mass). Thus, +Benedict took away the excommunications of the 4 sspx bishops and "freed the latin mass" through his 2005 motu proprio. Both these actions were unnecessary, since the excommunications of the 4 bishops were bogus and the latin mass was always allowed by law, due to Quo Primum, which +Benedict admitted in his motu docuмent. So, these actions were just PR stunts, with the hopes of swaying the opinion of the new-sspx laity towards embracing new-rome and opening up a "dialogue" on reconciliation.
At the same time this was all going on, +Fellay started to crack down on all the priests/bishops in the society who did not want to make a deal with new-rome, who did not want to compromise on doctrine, and who did not want to betray +Archbishop Lefebvre's work to uphold Tradition and true Catholicism. Those priests/bishops who would not stay silent during +Fellay's betrayals, were exiled or forced to leave the society, until +Fellay had enough "yes men" to control the organization.
Those bishops/priests who were kicked out, many stayed together and formed what they called "The Resistance", which was meant to stay true to +Lefebvre's original stance towards heretical new-rome, and to oppose +Fellay's liberalism and to keep masses/sacraments available for those former sspx-laity who had also left the new-sspx, due to the gradual modernism and compromises which had crept into the entire society (from books being edited, to websites being censored, to articles disappearing, to sermons being modified, etc).
The new-sspx is to V2, what the Resistance is to Traditionalism. The new-sspx is a modernized version of True Catholicism, just as the Resistance is the same as the SSPX as founded by +Lefebvre.