I do know that the Russian nobility faced great terror under Ivan IV. The movie by Sergei Eisenstein, "Ivan the terrible" shows him as a benevolent ruler as far as people are concerned. I wish to know to what extent this portrayal of him is true.
First. Movies are not a good source to study history. Soviet Movies especially. And the least reliable of them (for the study of history) are those made in Stalin's epoch. This particular movie of Eisenstein was made with the explicit propaganda purpose to justify the state terror. Stalin's henchmen, if not himself publicly stated that they see analogies between Stalin's regime and that of Ivan IV.
Second. Ivan the Terrible terrorized not only the nobility and boyars. Most of the victims were ordinary people. Read about his sack of the city of Novgorod, for example.
Were people happy or not, I don't know, I cannot ask them. Perhaps some of those who did the looting, murder and torture were happy. Those whom they killed looted and tortured probably were not. And those killed left no writings and no folklore.
The case of Stalin is probably similar indeed. I knew a lot of people who lived under Stalin, and I witness that they were not happy with Stalin's regime. And you cannot ask the millions whom he killed. By starvation or otherwise. But if you talk to Russian people today, many of them will justify him and even glorify. One of the reasons is that they learn history from the Russian TV. Whose main purpose is to justify the modern bloody conqueror. The popular memory is really short.
Many people remember nowadays how North American Indians were exterminated. But who remembers the conquest of Siberia? Which started under Ivan IV.
Yes, it seems that common people were generally happy about Ivan the Terrible's rule, as far as we can tell.
Primarily, throughout folktales, the tsar is typically described as an “ally and protector of the ordinary people against their common enemies, and especially the boyars (noblemen)".
Ivan the Terrible did restrict the movement of peasants, and entrench the institution of slavery. But at the same time, he persecuted the nobles and apparently was seen as protecting peasants from exploitation. Thus, just based on the limited information we have, passed down through folktales, Ivan was seen as an ally of the peasants. Being terrible to boyars might be a compliment.
Even Ivan’s nickname has left a controversial legacy. The English word “terrible” is usually used to translate the Russian word grozny. Yet, grozny’s meaning is closer to inspiring fear or terror, threatening or awesome rather than sinister or cruel. Some believe the original intended sense could have been Ivan the Fearsome or Ivan the Formidable.