Feta cheese and ripe olives are the biggest difference I see in the Greek salads I get in my part of N Am. I've not been to Greece. Type of onion is not often grown in home gardens here. And feta cheese is a cube the size of that ripe olive.
But I spent a good 2 months in Israel back in the 70s. When I was on the kibbutz each day we were given 1 tomato, 1/4 green pepper, 1/4 med. onion, and 1 4" (i.e. little type) cucumber and a bit of oil. This we diced ourselves.
When I worked in the Kibbutz guest house, they diced the salad and added grated carrot just before meal time. A large bowl of this per table. It's been my fav salad ever since.
:C