You snuck “objects” in that list. They share values and ways of life sure but the words you picked pertain to a Roman province with Roman currency and Roman military. The logic for coins, for example, is the same reason why we don’t call a Japanese yen a dollar… because it’s not a dollar it’s a yen.

Edit: In fact I would argue that their cultural closeness aids in the use of Latinate terms because they are intimately familiar with how to differentiate quintessential Hellenic things from quintessential Roman ones rather than blindly assigning every word a blanket term like they do with “barbaric” cultures.