You can say "Greeks" but then you might want to also say "Spaniards".
These are nouns: Spaniards, Greeks (or Greek people), Turks, Englishmen, etc.
The other way is using adjectives: Spanish, Greek, Turkish, English, etc. In this case, you cannot use the plural. Adjectives stay singular in English.
So, you might want to pick one way and use it for both.
But both will translate the same way to Hungarian. The above distinction does not exist in Hungarian (most of the time), and also, adjectives can also be in the plural, almost acting as a noun.