What are the three forms of government by which Texas cities operate?

The three forms of city government in Texas are the
mayor-council, city commission, and council-manager systems.  These typically differ as
to who runs the executive branch of the city. 

In the first
form of government, the executive branch of the city is run by a mayor.  There can be
strong mayors who are elected separately by the people and are not part of the city
council.  They can typically do things like appointing various officials and vetoing
laws passed by the council.  There can also be weak mayors who are often part of the
council and are only selected to be something like a chairman of that
group.

In the city commission form of government, there is
no separate executive branch.  Instead, the various members of the city council each act
as the head of one particular part of the executive
branch.

In the council-manager system, the executive branch
is run by an unelected official.  This person is called the city manager and is hired
for his or her competence rather than being elected by the people.  This form is meant
as a “good-government” form that is more technocratic.