There may be many reasons to use a hyphen before the word 'Orthodox', but all canonical Orthodox Churches share the same faith.
You may have heard of the Greek Orthodox Church or the Russian Orthodox Church, or perhaps you have heard of the Antiochian or Alexandrian, or Romanian or Serbian Orthodox Church. Whatever the name you have come across before, the fact is that they don't really matter all that much. The only name that matters is 'Orthodox', as it is this that makes us what we are. The ethnic or national designations are actually mere descriptions of the cultural influences you may encounter in our services and in our communities.
“The name 'Russian' or 'Greek' when it comes to Orthodoxy must always be secondary, as it represents nothing more than a description. It is Orthodoxy itself that matters.”
After Pentecost, the apostles went out into the world. Tradition tells us that Mark, for example, went to Egypt, and that Thomas made it all the way to India. Whatever the case, what we know for certain is that the Faith spread quickly around the Mediterranean and beyond, and that as it did, it encountered many cultures. These cultures not only received the Faith; they also gave back, and so it was that even where the Faith was fundamentally the same, the language and traditions by which it was expressed was different.
This historical reality is what gave rise to the different jurisdictions we have in Orthodoxy today. And as the Church has moved West, into countries where it has not been known before, this has sometimes given rise to confusion. But living in a country with different regions is really no different. A single country may boast different regions, each with their own traditions, but the idea of being part of a single country still gives life to that region: it feeds that region and is fed by it in turn. The region may even use a different language to the rest of the country, but its place in the country and the mutual exchange between the two is undiminished. Whether the Orthodox Church speaks Greek, then, or Russian, or Romanian, or English; whether it includes rituals in one place that it does not in another: these things are fundamentally insignificant. What matters is whether or not the Church is Orthodox, and whether or not it is recognised by the other Churches as being so.