Cement, or Portland cement, is a dry powder made from limestone and other materials. It is burned in a kiln and then ground finely. Cement reacts chemically with water to cause concrete to harden. There are several different types of Portland cement, designated as Type I, Type II, etc. The concrete is delivered in a plastic, unhardened state.
Cement is an ingredient in concrete.
Flyash is a byproduct of coal-burning power plants. When used properly in concrete, it improves the quality of the mix and saves money. Concrete with flyash will typically have a higher ultimate strength, although early strength will be lower than with straight cement. That is rarely the problem. More often the problem is not enough cement in the mix.