The "Greek Orthodox" Church is one of many "Eastern Orthodox" churches. As an example, my baptismal certificate (From a "greek orthodox" church) actually says that the said baptized person of the "Eastern Orthodox Church", etc etc. I always was happy it said that because it was testifying that we are all the same in doctrine and practice, which we are --- and it was an anti-ethnocentric/phyetic statement, though it's so hard to convince the tribal people that this is truly the case.
As a quick aside too though, since it is an "eastern" christian church there is, in a general sense, a similar meaning of "Greek Orthodox" as being easterner (and thus a surrogate term for EO) in the sense that the Roman Catholic church isn't roman (even in the modern day) but they call themselves that.
The problem in the West is that people are so woefully un/mis/mal-taught about the faith that even Orthodox themselves in so many cases are oblivious to the fact that Greek=Russian=Romanian=Serbian=Ukrainian Orthodox, and on and on and on --- it is one faith, the One, Holy, Catholic and Apostolic Church mentioned in the Niceno-Constantinopolitan creed. It turns out that the "Orthodox" church is actually, also, the true Catholic church! (-:
As a quick aside too though, since it is an "eastern" christian church there is, in a general sense, a similar meaning of "Greek Orthodox" as being easterner (and thus a surrogate term for EO) in the sense that the Roman Catholic church isn't roman (even in the modern day) but they call themselves that.
The problem in the West is that people are so woefully un/mis/mal-taught about the faith that even Orthodox themselves in so many cases are oblivious to the fact that Greek=Russian=Romanian=Serbian=Ukrainian Orthodox, and on and on and on --- it is one faith, the One, Holy, Catholic and Apostolic Church mentioned in the Niceno-Constantinopolitan creed. It turns out that the "Orthodox" church is actually, also, the true Catholic church! (-: