Appropriate mixing, temperature, pH, O2, foam controls and pressure controls can be made simultaneously in the fermenter. There is no need for an additional device and it is suitable for sterile operation. Sterilization is done by autoclave in the fermenter, this is not possible in the magnetic stirrer. The main purpose of the fermenter is to facilitate the fermentation and to carry out the development of organisms such as bacteria and yeast under sterile conditions. In the magnetic mixer, only mixing is done. No heating (except for the heated magnetic stirrer). Both automatic control and manual control can be done in the fermenter.
The main differences are that fermenter is more sophisticated, as it usually has more controls and sensors, such as DO, temperature, pH, etc., while a mixing tank usually use mechanical force to mix things, so a mixing tank doesn't need the advanced controls to make the microbes/cells happy inside the vessel. Here is a more detailed article about their differences: