How does "Islamic revolution" resemble other waves of revolution (Communist peasant rebellions in the 20th century, national revolutions in Europe in the 19th century, democratic revolutions in the 18th and 19th century)? How does it not? What accounts for the differences?
I would argue that Islamic revolution is fairly similar in important ways to the other types of revolution that you mention in this question. There are, however, some important differences.
The major similarity is that all of these are revolutions that have been interested in changing their societies in profound ways. This is something that is common to all true revolutions. The revolutions begin with the idea that there is something that is fundamentally unjust about the society as it is. They then try to do away with that injustice.
Another major similarity is that all of these revolutions were popular revolutions that were controlled (or at least led) by elites. In the communist revolutions, for example, there were “vanguard parties” that organized and focused the revolutionary energy of the common people. Similarly, in Iran there was Ayatollah Khomeini who acted as the leader of the masses of common people who were unhappy with the Shah’s rule.
Thus, we have revolutions that were similar in fundamental ways. They all were driven by deep dissatisfaction with the status quo. They were all made up of masses of common people who were led by elites.
At the same time, however, there are differences between these sorts of revolution. The major difference is in how inclusive the revolutions have been. Some of the revolutions have been very inclusive. A national revolution will welcome anyone who is of the correct nationality. A democratic revolution will welcome anyone who is willing to accept the ideas of democracy. These revolutions do not necessarily exclude anyone. By contrast, revolutions like the Islamic revolutions and the communist revolutions are more exclusionary. Communists will never accept members of the capitalist class and will often act very violently towards them. Islamic revolutions have tended to be very intolerant of other religions or even of other interpretations of Islam. These differences come about because of the nature of the ideologies that drive the revolutions.