It's more grey. The Macedonians were sort of Greek, and sort of not.

The language the Macedonians spoke was related to ancient Greek, but had dialectical differences--it seems that there were pretty predictable consonant differences, though there's not a huge corpus of Macedonian writing. Herodotus tells the story of Alexander I of Macedon (not Alexander the Great--that was Alexander III), who was initially barred from competing in the Olympic Games, as that right was reserved for true Greeks. He claimed that his ancestry was from Argos in Greece proper, and was allowed to compete.

There were also political differences. Macedonia was not organized into city-states, as Greece itself was, but instead had a ruling dynasty from whom kings were chosen as well as powerful regional lords. Strong kings who could overawe the nobility had a lot of manpower at their disposal; weak kings had trouble keeping the nobility under control.

It depends on the period you're considering. The Macedonians under Philip and Alexander would have considered themselves culturally Greek. Philip championed geek culture and sought to assimilate its values with those of his people. That's partly the reason why Philip formed league with Greek city states rather than destroy them. (He also needed an immense force to take out the Persians) Alexander continued in his father's path and embraced Greek culture. His tutor was Aristotle, so I'm sure that had a profound influence on his appreciation for Greek culture.

Really what I've said is an incredibly basic overview on the matter. I'm on a phone and typing out a more comprehensive narrative would be tough. If you're interested though Ancient Greece by William Dunstan is a solid book for an overview of Greek history and culture.