My essential understanding is that the Phoenicians were the aftermath of the Mycenaeans after their society collapsed.
Dang thing reads like a book report...
The Greeks were never under the same rule until they were conquered by the Romans. Philip of Macedon and his son forced some of them into the League of Corinth and tried to boss them around (Alexander even destroyed the city of Thebes) but some of the Greeks of Greece proper remained independent (as well as the western Greeks in Italy, Sicily and elsewhere).
Just like the Phoenicians didn't call themselves Phoenicians, the Greeks didn't call themselves Greeks. That comes from the Roman name for them--they called themselves Hellenes.
There was an interesting article on You Tube about “The Sea Peoples” of about this era who rampaged over the Levant. The Egyptians fought with them but their origin is evidently still obscure.