The Mongols invasion into Russia territory was around 1219. They entered Russia and the effect was catastrophic. Mongols looted and destroyed the cities, killed people and slave entire families.
After the invasion, Russia modified important aspects of its culture like language, art and religion. The Princess of Russia an the assemblies lost political authority which allowed the Orthodox church to rise as a national identity.
The Mongol's invasion of Hungary territory on 1241 annihilated the Hungarians by the hands of Genghis Khan's successors. On of the differences with the Russian invasion is that Russia was not exterminated. There were some influences and changes in many symbols an parts of the culture. But in the case of Hungary, they were completely destroyed.
The demography of Hungary changed, as well as the ethnic map between the Carpathians and the Danube. The remaining Slavs and Cumanians were absorbed by the Romanians