First of all Hello all forum members!
I know this thread hasn't been used for a while, but this is a history forum, so here I go.
What is important to say about the greek/macedonian influence in the middle east and any territory that was conquered and included in the vast Macedonian empire of Alexander the Great is the fact that it can still be traced. Although it must be said that because of the short-lived reign of Alexander and his ill-fated succesors, the influences today are minute and can be considered under the title "Believe it or not!".
This is more then evident in some remote areas of Pakistan and Afghanistan. The remnants of a "strange" tribe that lives in the mountain regions, speaking a strange language, celebrating "foreign" (for the region) rituals and having physical characteristics completely different from any neighboring peoples (namely blonde hair and blue eyes) is a startling example of a living history example. The Kalash people of Pakistan are a living link to the famed conquering expedition of Alexander the Great, some 2300 years ago.
As for the origin and relation of Macedonians and Greeks, from all I have read on the subject it seems quite clear that Macedonians were not Greeks, but first-door neighbors, so to speak that were always there, but were too weak and poorly organized until the rule of Philip II.
As famed historian Peter Green says in the intro of his book: Alexander of Macedon, Chapter: Philip of Macedon
"The story of Alexander the Great is inexorably bound up with that of his father, King Philip II, and with his country, Macedonia. Philip was a most remarkable and dominating figure in his own right; while Macedonia, as has recently been observed was the first large territorial state with an effectively centralized political, military and administrative structure to come into being on the continent of Europe. Unless we understand this, and them, Alexander's career must remain for us no more than a progress of a comet, flaring in unparalleled majesty across the sky: a marvel, but incomprehensible. Genius Alexander had, and in full measure; yet even genius remains to a surprising extent the product of its environment. What Alexander was, Philip and Macedonia in a great part made him."
In a nutshell, Macedonians became very strong because of Philip's genius of gaining territories that yielded a steady supply of gold as well as the reform of the phalanx that gave the Macedonians an unprecedented advantage over Greeks, Persians and anyone else they encountered on the battle fields.
So, they invaded and conquered Greece, sealed by the battle at Chaeronea.
It would take years, many rebellions and a foreign power i.e. Romans to put an end to the Macedonian hegemony over Greece. And this didn't mean liberty for the Greeks, but rather change of rulers from Macedonian to Roman.