A working division can be made into:
Greek architecture before Alexander the Great
Only Greek Architecture before Alexander (who died in 323 B.C.) carries any ethnic designation. The ancient Greeks were notoriously dismissive of barbaroi, those who spoke Greek non-natively or (even worse!) not at all. The incredible conquests of Alexander and the subsequent application of a veneer of Greek city states to a base of Egyptian, Semitic, and even Iranian populations produced an important change. Though Greek-speaking remained the touchstone of whether one was a member of civilized culture or not, the ethnic diversification of the Hellenistic world is clear. The formal elements of classical Greek architecture were applied to temples for gods never worshipped in Greece.
The Romans can be seen as the latest Hellenistic empire. Pre-imperial architecture is more or less Etruscan with some Greek elements. By the time the Romans conquered mainland Greece in the 2nd century B.C. they were importing Greek craftsmen to build major public buildings. The term “Roman Art” and “Roman Architecture” has no ethnic meaning of “Italic Romans.” Most art historians assume that it has the ethnic meaning of “Greek-speaking slave” or “Greek-speaking free laborer,” in fact.
The elements of classical architecture turn out to be just that -- elements that can be applied in radically different architectural contexts than those for which they were developed The classical orders -- doric, ionic, and corinthian -- have a kind of meaning or stylistic developmental history in 5th century B.C. Greece that can be passed over or shifted in 1st century A.D. Gaul, which is why they have been revived over and over again since then.