Were they independent of the city state that founded them, effectively making them just a new city, or was it like imperial colonialism of the industrial European states where the original sponsor controlled it from afar.
The former! I've explained this in more detail here. Modern scholars argue that the word "colonies" is inappropriate because we're talking neither about Roman-style colonia nor about the territories of the age of colonialism. They tend to prefer the more neutral "overseas settlements", which is more true to the Greek apoikia ("away-from-home").