I don't think it would be appropriate or edifying to you, especially in light of your current situation, to get into any kind of serious discussion with regard to the differences. But a brief overview might look something like this...
The True Orthodox Church (TOC) of Greece has the position that they are "walled off" from the innovators, them being the "healthy part" and the innovators being the "ailing part" of the same body, both having Grace.
They say: "Persons in error concerning the correct understanding of the faith -- and thereby sinning, but not yet judged by an ecclesiastical court -- are ailing members of the Church"; They say: "Orthodox Christians have an Evangelical and canonical right to wall themselves off: that is to say, to break ecclesiastical communion with and commemoration of a Bishop who preaches 'heresy' 'publicly' 'and bareheaded in the Church,' or who is blameworthy, in that he errs unrepentantly 'in point of piety and righteousness,' as the Thirty-First Apostolic Canon states —namely, when the Bishop acts 'contrary to duty and justice,' as Zonaras the canon lawyer explains. If a Bishop or clergyman is 'evil' 'with regard to the Faith, leave and abandon him, not only if it be a man, but even it be an Angel come down from Heaven,' says St. John Chrysostomos."
There is considerable merit through the history of the Church to "walling off" under certain circumstances.
Since the TOC considers itself to be joined to the "ailing" part of the church, it does not set up parallel structures, churches, and bishops in Greece, and does not have an "Archbishop", just a "President" AFAIK. It is non-canonical to set up parallel structures.
The Genuine Orthodox Church (GOC) of Greece has very close and fraternal relations with ROCOR, although there is no longer any intercommunion since the ROCOR has actively communed with the Serbians.
The GOC holds the position that "those ailing in the faith" cannot be members of the Church and so they have fallen away. Without citing canons, this is supported by St. John Cassian who says, "he who does not confess the faith of the Church is outside the Church." The same is confirmed also by Patriarch Jeremias II of Constantinople: "Members of the Church of Christ are wholly devoted to the truth, and those not wholly devoted to the truth are not members of the Church of Christ." St. Cyrpian of Carthage teaches: "Just as the devil is not Christ, although he deceives in His name, so also such a one cannot be accounted a Christian as does not abide in the truth of His Gospel and Faith." And one last example is St. Gregory Palamas who explains: "Those who are of the Church of Christ, the same are of the truth; and those who are not of the truth, the same are also not of the Church of Christ..."
So the short of it is, the only difference is that the GOC, as well as all the other "Old Calendar" Churches in Greece, Bulgaria, Serbia, ect. consider the syncretist innovators to be Graceless, while the TOC does not.