Alexander the Great--Greek or Macedonian?

I have heard this question asked in some form or another for a long time.  My answer has always been that Macedonians were Greeks, just a little out of the Athens-Sparta-Thebes mainstream.  Today's Former Yugoslavian Republic of Macedonia calls itself a Slavic nation and claims Alexander as its national hero.  I don't blame them, but back we go to the original question--Were Alexander's Macedonians Greek or something else?

I was reading Arrian,s Campaigns of Alexander detailing Alexander's conquest of Persia and invasion of India.  In it I find an interesting passage, a letter from Alexander to the King of Persia at the time, Darius: (emphasis is mine)
       "Your ancestors came to Macedonia and the rest of Greece and did us great harm, though you had suffered no harm before then." (Arrian, 2.14.4)

It sounds as if the Macedonians considered themselves Greek and, of course, most of Aleander's army was Greek.  Sparta's attack in 333 BC on Antipater back in Greek while Alexander was crossing into India seems to fit the pattern of Ancient Greek history where the reigning hegemon is attacked when preoccudied somewhere else.

Something to think about as another thunderstorm rolls in!