The best way to start an answer here is always the academic equivalent of a shrug emoji:

“It is still unclear why they called the Hungarians ‘Turks.’” (Kaldellis, 116)

There is some logic behind it though: “Tourkia” was simply the place where Turks lived, and “Turks” were pretty much anyone from the central Asian steppes.

In the classical/late antiquity periods, the steppe warriors that the Greeks and Romans were familiar with were called Scythians or Huns, and since Byzantine authors loved to use classical terminology even if the terms weren’t really accurate anymore, so throughout Byzantine history, all steppe peoples could be called Scythians or Huns.

The actual ancient Scythians and the Huns from the 4th/5th centuries probably weren’t related to each other at all; Scythians were Indo-European or at least seem to have spoken an Indo-European language, something like Persian (and so ultimately related to Latin and Greek) while the Huns were probably Turkic and spoke a completely unrelated language. The Byzantines first became aware of people who called themselves “Turks” in the 6th century when the Göktürks settled around the Black Sea, so “Tourkoi” became another category that could describe steppe peoples.

More nomads from the steppes showed up over the centuries, notably the Khazars, Cumins, Pechenegs, and Magyars/Hungarians, among various others. Meanwhile, the Persian/Arab neighbours of the Byzantines were also familiar with the central Asian peoples who bordered them, and in Persian and Arabic they were always called “Turks”, so the Byzantines also adopted this generic term for peoples on opposite sides of the empire, who maybe weren’t very closely related, but nevertheless came from, well...out there in the steppes somewhere.

What we call Turkey today was Byzantine Anatolia. By the 11th century the Seljuk Turks, who were originally another group of nomads from central Asia, had migrated into Persia and the Middle East. They were well known to the Byzantines, and after the Battle of Manzikert in 1071, and even more significantly after the Battle of Myriokephalon in 1176, the Seljuks began settling in Anatolia. There were other Turkic groups living in Anatolia along with them, and eventually one of them, the Ottomans, replaced the Seljuks and conquered the Byzantine Empire, which is how Anatolia came to be known as “Tourkia”, or Turkey today.

But before the Seljuks and Ottomans arrived, “Tourkia” was instead to the north, on the shores of the Black Sea, and by extension anywhere north of the Danube, since that’s where most of the Turkic peoples settled, as far as the Byzantines were concerned. Since the Byzantines did distinguish between different groups of people with different names (the aforementioned Khazars, Cumins, Pechenegs, also the Uzes, the Bulgarians, among others), the question is, why did they usually not call the Hungarians by their own name? They knew their name - there are certainly Greek versions of “Magyar” and “Hungarian” - so why did they just consider them generic “Turks”?

At first, it was possibly because the Hungarians were actually the weakest of the steppe nomads in the north. In the 10th century the Pechenegs were the major power around the Black Sea and the Byzantines could count on them to prevent the Rus’ (who were Slavic/Scandinavian) and the “Turks” from attacking the Empire.

“The tribe of the Turks, too, trembles greatly at and fears the said Pechenegs, because they have often been defeated by them and brought to the verge of complete annihilation. Therefore the Turks always look at the Pechenegs with dread, and are held in check by them.” (De Administrando Imperio, pg. 51)

To summarize the subsequent history of the Hungarians very briefly, they continued to move west and began raiding Europe, all the way to Italy and Spain, until they were defeated by the Germans at the Battle of Lechfeld in 955. Afterwards, they settled down for good in the Carpathian basin, roughly the area of the modern country of Hungary. In 1001 Stephen I was recognized as King of Hungary and started (or continued) converting the Hungarians to Christianity.

Some parts of the “Crown of St. Stephen” might date from Stephen's time, but the Greek parts are definitely a bit later, from the 1070s, as they refer to Geza I as “Krales Tourkias”, kral (borrowed from the Slavic term for “king”) of the Turks. Maybe by this point, since the Hungarians had become the most powerful of the Turkic peoples to the north, the Byzantines simply considered them the lords of all the Turks?

But as Kaldellis noted, we really just don’t know why. What we do know is that the Byzantines considered the area to the north and west of the Black Sea to be “Tourkia” and that the land was inhabited by central Asian nomads (whether they were actually Turks or not). Turks from central Asia also settled in Anatolia but that region became “Tourkia” much later.

Sources:

Rustam Shukurov, The Byzantine Turks, 1204-1461 (Brill, 2016)

Anthony Kaldellis, Ethnography After Antiquity: Foreign Lands and Peoples in Byzantine Literature (University of Pennsylvania Press, 2013)

L.S. Tóth, “The territories of the Hungarian tribal federation around 950 (some observations on Constantine VII’s ‘Tourkia’),” in G. Prinzing and M. Salamon, eds., Byzanz und Ostmitteleuropa, 950–1453 (Wiesbaden, 1999)

Constantine Porphyrogenitus, De Administrando Imperio, ed. Gyula Moravcsik and trans. R.J.H. Jenkins (Dumbarton Oaks, 1949)