Mediterraneans & Nordics do look far more alike than popular caricature tends to suppose, a fact noted by the physical anthropologist Carleton Coon & reiterated by British zoölogist John R. Baker (Race (1974). The distinction between the two is, in practice, frequently subtler than commonly supposed. John R. Baker goes so far as to say that even expets in the field often fail to distinguish accurately between Nordic & Mediterranean samples when presented with them directly.
Son... Slaves looked so similar to Greeks, that Athenians beat up their fellow citizens, mistaking them for slaves.
This adds up, as most slaves were other Greeks. Genetic data also corroborates that there was no genetic differentiation between Greeks of different social status.