The referendum is due to take place on 23 October
Two groups have been set up to campaign for the different options in next month's referendum on how Stoke-on-Trent should be run.
However, despite their differences in opinion the two groups share the same name - People's Choice.
The government told Stoke to change its existing system where the elected mayor and chief executive make all decisions.
It offered it the option of an elected mayor with a cabinet or an elected council leader with a cabinet.
The public will be asked which option they prefer on 23 October.
The "no" campaign, calling for the elected mayor and cabinet system, is being run by former councillor Paul Breeze.
Current councillor Mike Barnes, is leading the "yes" campaign, which is calling for a leader and cabinet.
Both groups have accused each other of choosing the same name to confuse the public over what is already a complex issue.
If the city votes yes to the elected leader system, it will be installed from May 2009.
However, if the system is rejected, the elected mayor and cabinet system will be introduced.
The city is currently the only local authority in England to have its existing political system.