Well, this is a difficult question as Hellenic identity originally based itself around ethnicity (whether a people were descended from Hellene) and tracing the roots of a people back to their traditional origins which stretched back in time to mythology was the most important factor, while this did remain a facet of Greek identity, in later times culture came to be the defining element of Hellenistic identity.

Macedonia appears to have been very similar to Greek states in culture, architecture and society, although it retained many archaic traditions after they had been abandoned or otherwise changed elsewhere as well many unique traditions of its own. Attic Greek as a language was the lingua franca throughout the Aegean, before transitioning into Koine Greek during the Hellenistic Period, and this apparently held true in Macedonia as it was the language of the court and apparently the only primary language, although there are few surviving records of the ancient Macedonian language as it had a primarily oral tradition and fell out of wide use. The Macedonian language does appear to be a dialect of Northwest Greek, especially Doric. After entering the Panhellenic League and particularly the conquests of Philip II and Alexander the Great there was a large amount of syncretization between Greeks and Macedonians although there were still clear distinctions and at times tensions present even in the armies of both. Alexander, for instance, was the first of his dynasty to permit Greek generals to hold command in his army, but several anecdotes describe patriotic competition and rivalry between Macedonian soldiers and their Greek counterparts.

Ancient sources are actually somewhat inconsistent when they describe the Macedonian ethnicity, Herodotus in his Histories relates a tradition of Greeks who wandered until some settled around the Peloponnese and became known as the Dorians and others settled around Pindus and became known as Macedonians, but he also distinguishes between Greeks and Macedonians in his work by describing the Argead royal family as Greeks who ruled over Macedonians. And it was agreed that the Argeads had a claim to Heraclean descent, but this was still contested and even so, only extended to the royal line, leaving the origins of the Macedonians as a people uncertain. Later authors like Apollodorus considered the Macedonians to be a barbarian people and during the tensions between Athens and Macedonia there was an apparent increase in perceived disparity between Greeks and Macedonians. Even during the Hellenistic Era following the establishment of Alexander's Empire and its subsequent division by his Macedonian generals there continued to be Greek uprisings and resent over Macedonian rule for centuries.

Romans however did not distinguish Greeks from Macedonians, and counted them as the same people. This is evidenced in the works of authors like Plutarch, and Livy which count them as stemming from the same tribe. Persians apparently also gave them the same name (Yauna) due to the fact that they shared a language, although they did distinguish them by their region.

The actual question of what defines Greek heritage, ethnicity or culture and upbringing, is a political one and seems to be getting a bit of scrutiny at the moment, which sadly, always seems to detract from the historicity and objectivity of a question, but it is pretty safe to say that the Greek identity evolved slowly and its definition changed with time, external factors, syncretization of foreign traditions, and internal politics, so the place that the Macedonian ethnicity held naturally changed as well.

Sources:

Herodotus' Histories

Plutarch's Parallel Lives

Livy's Histories

The Oxford Encyclopedia of Ancient Greece and Rome

But there are many more modern sources with varying opinions even on how Macedonians were perceived in a given time period, based mainly on these works and there are archaeological findings such as the Pella Curse tablet which shed light on this topic, so I would advise doing your own research if you want the most in depth answer possible.

Edit: I also wanted to mention that even among the Greek city-states there was not always a unifying "Greek" identity, particularly in early history and Greek culture as a whole is more of a synthesis than a standard tradition, bound together by common myths, practices, and language, as well as ethnic ties. A common Greek identity often surfaced in opposition to foreign pressures such as threats from Persia and Rome, and by the time of the Panhellenic league the states were a lot more close knit than they were in the Mycenaean Age. From this, foreign practices from places such as Persia, Egypt and India found their way into Greek culture leading to a Hellenistic identity unique from the Hellenic, as Greek culture flourished in the Hellenistic Period it also absorbed and perpetuated many Near-Eastern traditions in the kingdoms carved out of Alexander's conquests.