No. A CCE is not the same as a City- or municipally owned utility ("muni"). In a muni, a City purchases the electricity transmission and distribution system, i.e., the power lines and related infrastructure, from a utility through what is called a condemnation process. The city also buys the electricity to deliver to homes and businesses and provides all billing and customer service functions. In this case, the muni operates just like an investor-owned utility but reports to their local governing body rather than shareholders.
With CCE, the utility still owns and delivers the electricity through its own power lines, but the CCE purchases electricity on behalf of local electricity customers and sets generation (supply) rates for its customers. In a CCE, customers can opt out of the CCE program if they wish to keep the utility as their electricity provider, which is not the case with a muni.