There is this funny anecdote, once some Greek soldiers took control of an Ottoman island and stationed themselves in the main square. Some children came running and said they wanted to "see the Hellenes (Greeks)", the soldiers replied "but aren't you Hellenes yourselves?" "No", said the Children, "we're Romoi (Romans)". I can't provide a citation for this story, but it illustrates how difficult it is to use words like "Greek" or "Greece" to describe the past. Often, people had a very different view of themselves than they do today. In the Byzantine and Ottoman world, group identity revolved around tribal/clan descent and religion, ethnicity was really in the background and national identities, like Greek, were either nonexistent or not widely popular.

It's hard to say then how Greeks were treated under Ottoman rule because people did not think that there existed such a place called Greece, the whole of The Southern Balkans was then part of one country: Rumeli. Equally fictions was the idea of the Ottomans being a Turkish empire. the Ottomans themselves saw themselves as a continuation of Byzantine rule, the Sultans claimed descendant from Alexios I and were known throughout the Islamic world as Qaysar-i-Rum (Caesar of Rome), a large number of Greek speaking Byzantine families made up the core of the early Ottoman state. When it came to stocking their bureaucracy, the Ottomans had a preference for people from the Balkans, especially Muslim converts, and the janissary slave system actually helped foster a Christian middle class as these slaves used their position within the imperial hierarchy to benefit their families and install them in high office. The Greek speaking Phanariotes are probably the most notable example of this. But it wasn't all fine and rosy, ordinary Greek speaking Christians, or Urums as they were then called in Turkish, were subject to a series of humiliating restrictions, which included a ban on constructing new churches, owning weapons or riding horses in the presence of Muslims, however in many places these formal rules were never strictly enforced if not outright ignored.

During the mid 19th century, the empire underwent reforms that drastically changed the government's attitude towards Greek Christians. The Gulhane edict of 1839 declared all religions equal, eliminating discriminatory laws to the extent that calling non-Muslims kaffir or gavvur (infidel) was a punishable crime. While Greek Orthodox Christians had always had the right to be governed by their own religious laws through the Church, now each religious minority (millet) got their own parliament and constitution to govern their affairs, as well seats reserved in the Ottoman parliament. But, these reforms also created new tensions as Christians did not want to be drafted into the army, nor did Muslims want to serve under Christian officers and violent massacres to suppress uprisings led to discontent. The Ottomans also promoted a kind of pan-nationalism, all citizens of the empire were now considered Ottomans, regardless of their religious or national identity, and had equal rights under the law. The whole empire, from Thessaloniki to Cairo, was now part of one big umbrella nation. As we all know, the empire's collapse during WW1 was pretty brutal, genocide, ethnic cleansing, mass deportations. Nicholas Doumanis researched the opinions of ordinary Greek Muslims and Christians, he found that they tended to idealise the pre-war empire, remembering how they'd lived well together. As much as these two religious communities had their differences, and those differences did sometimes become violent, they had found a way to coexist together in a multi-ethnic, multi-religious society, they celebrated each other's holidays and even worshiped the same saints. The last thing I will mention here is the Ancient Greek heritage, Muslim culture was greatly indebted to Ancient Greek culture and it's not surprising then that Socrates, Plato and Aristotle were seen as prophets and wise sages. The Ottomans loved to connect themselves to the Ancient and Byzantine past, the Sultans themselves claimed descent from Emperor Alexios I Komnenos and the empire was officially called the Roman Empire (Devlet-i-Aliye-i-Rum).

Really, there's a lot to say on this topic. We're talking about 500 years of history here. So here are some further readings I can recommend if your interested:

Before The Nation by Nicholas Doumanis (focuses on Greek Christians in the late empire)

An Ottoman Mentality: The World of Evliya Çelebi by Robert Dankoff (translation of the traveller Evliya Çelebi, who describes Athens under the Ottomans)

State Faith and Nation in Ottoman and Post-Ottoman Lands by F F Anscombe (looks at how religion shaped sectarian identities in the 19th century as well as the successor states of the empire like Greece, Turkey and Yugoslavia)

Black Athena: Vol 1 The Invention of Greece by Martin Bernal (controversial book, looks at how Westerners invented the idea of Greece and how they deliberately ignored it's connection to other Eastern civilisations like Ancient Egypt)