I would argue that there are actually four major structural forms of municipal government in the United States. I will include all four in this answer. Please check your textbook or your class notes to see which three your instructor considers to be “major.”
These four forms are 1) council-manager, 2) council-mayor with a weak mayor, 3) council-mayor with a strong mayor, and 4) commission. I would say that the first three of these are the major forms because they are the most common. However, some people (as in the link below) would put the two council-mayor systems together as one form and include the commission form. I would not include the commission form because it is so rare in the United States.
All of the forms of government are basically democratic. This is their most important common characteristic. The other main important similarity is that, in all of these forms of government, the legislative function of the city is performed by a city council. So, all of these types of government have a city council that is elected by the people and which is in charge of passing laws for the city.
The major differences between the forms have to do with the executive branch of government. In the council-manager system, the chief executive is an appointed city manager. That person is in charge of administering city government. They do not have a role in the legislative process (no veto power), but they are in charge of running the city. In the weak mayor system, the council has a great deal of power over the executive branch. It, rather than the mayor, typically has the power to appoint and remove heads of city departments. The mayor generally has very little power and may be something of a figurehead. In a strong mayor system, the mayor really is the chief executive. The mayor often has veto power over laws and is responsible for running the executive branch. In the commission system, there is no chief executive. Each member of the council typically serves as the head of one or more of the departments of city government.
Thus, all of these forms of government are democratic and have a city council with legislative powers. The differences lie in the nature of the executive branch.