Godol is a relative term; it means someone who stands out among his generation in greatness, which is measured in terms of Torah knowledge, and righteousness. There is no measurable threshold beyond which you are categorically a “godol”, like there is when a person gets a medical degree and becomes a “doctor.” Being that the term is relative, different people apply it to different levels for people, and even among those who are commonly referred to as Gedolim, they are not all the same. Rav Shach was a Godol, but he was not the Chazon Ish, for example.
You will not find the phrase “posek hador” used anywhere in any meaningful way. The Tzitz Eliezer uses it all over the place in his titles, and either the Teshuvos Maharshal writes it among the titles to the Ramah, or the Teshuvos Ramah about the Maharshal. I forget. But in any case, the title connotes no halachic status.
Rav Moshe isn’t always the final word in America either. Roshei Yeshiva and Poskim, such as Rav Hutner, Rav Eli Meyer Bloch of Telz, the Debreciner Rav, the Chelkas Yaakov and others, sided with the Satmar Rebbe over Rav Moshe regarding the obligatory size of a mechitzah in a shul, and/or the permissibility of artificial insemination, which were the two big disagreements that those Gedoim had in halacha. It was indeed Rav Hutner who approached the Satmar Rav asking him to write a refutation to Rav Moshe’s psak about the Mechitzos.