The Turks and the Russians never had a perfect relation. Constantinople was ofc the 'Capital' of the Eastern Orthodox Church for centuries. The fall of Constantinople to the Islamic Turks had a huge prestigious effect. The Turks had the intention to march even further and conquering more Orthodox land on the road [certainly in the Black Sea area].

The Rise of Russia meant the Rise of an Orthodox and Slav super power. The Balkans, now dominated by the Turks, were part of the Slav and Orthodox homeland. The Turks on the other conquered large part of Europe in, near, and around Russia [also via the Mountains of the Caucasus for instance] but were halted. This meant the stagnation of the Ottoman Empire.

Centuries of conflict and tensions passed on with Russia wanting to control the Balkans again as they saw it as Slav and Orthodox land. The weakening of the Ottoman Empire gave rise to national aspirations and interests in this region. They actively fought and supported Slav and Orthodox armies to chase away the Ottomans [and the Turks supported Muslim groups in the Caucasus for a long time]. This also inspired the Russians to finish their 'Historic Mission' and remake Istanbul into Constantinople ofc. The Russians actually thought for a long time that they could only reach this as a result of a large European war [because even when stronger then the Turks the other super powers did not allow them to conquer too much as the Crimean War shows]. The Russians still have to wait for this but they did succeed in actively defeating the Turks in large parts of Europe.

Turks were actually all over the place what with the various post-Mongol hordes and it wasn't until Ivan the Terrible started expanding Russian territory southwards that it became a problem with the Turks. He kicked the Astrakhan Khannate out of the Volga river and basically humiliated the Ottomans who never forgave them. Both sides went to war every hundred-or-so years with mostly Russian victories.