Alexander the great, Macedonian or Greek?

[King Jan III Sobieski]

He was "Alexander of Macedon", after all. I always considered Macedonians greeks...Greeks with a small "g". They were ethnographically Greek, but they were also a distinct people. Kinda like Spanish and Portugese, or Croats and Slovenes...for all intents and purposes, the same people, but different... or something like that.