Upvote:4
Present day linguists do not consider the two peoples related. There was once a theory that they were related, but it has been very far out of favor for half a century now.
However, there was a historic time when the two cultures intertwined, and this could possibly be what you are thinking of. This is the history of what is now the European nation of Hungary.
Sometime around 1 BC a group of Uralic (Finnish?) speakers probably living in Siberia near the Urals started to develop a very different culture, likely borrowed from their Altaic neighbors: Horse-based Steppe pastoralism. As their language developed, they also picked up a fair amount of Turkic words from those same neighbors. (These are the same set of borrowed words that fooled early linguists into thinking their language families might be related.)
The steppe horse culture the Hungarians and their Altaic neighbors engaged in requires a certain type of land - grasslands. The furthest west area in Eurasia that has large amounts of appropriate grassland turns out to be in present-day Hungary, and that is where the Hungarians chose to settle at the end of the 9th Century. To their beleaguered European neighbors they behaved like Huns, not Finns, so they were called "Hungarians".
The next furthest west area in Eurasia with a large areas of grassland are in central Anatolia. That is where some of their former neighbors, the modern-day Turks, ended up settling down.