The correct answer is - The Mongols killed many people but did not remain in Hungary for long.
The Mongol invasion in Eastern Europe was quick and effective one, but it was also short lasting in the majority of it. Lot of people were killed by the Mongols, be it soldiers or civilians, and that was the case in both Russia and Hungary. The difference was that the Mongols came to Hungary, managed to defeat it, killing lot of people in the process, but because of problems back in the homeland they had to retreat shortly after, thus they abandoned the Hungarian territory. With Russia was another story. The Russians were under Mongol rule for much longer, and even when the Mongol Empire divided into multiple hordes, they still managed to control Russia. Lot of Russians died in the process, and all the attempts for pushing the Mongols out were quickly suffocated. It was only after the Mongol hordes started to lose power and became much weaker, that the Russians managed to defeat them and push them out of their territory.