These are two services that are often confused with each other. A transmission flush service uses a machine that hooks up to the system's fluid lines and uses the vehicle's power to flush the old transmission fluid out of the system. This means almost a complete fluid exchange, but the service usually does not include replacing the transmission filter (where equipped).
Alternatively, a transmission service, also known as a fluid change, involves dropping the transmission fluid pan and replacing the filter, gasket, and the fluid that drops out. While this service replaces a large percentage of the fluid, it does not replace all of it. It does, however, result in a new in-line fluid filter.
In many cases, it is better to have a transmission service done versus a full transmission flush in older engines with higher mileage. Flushing an older transmission can result in harmful sediment getting stuck in the transmission's solenoids.