A Manual starter means that the control of it, i.e. how the motor is turned on and off, is done MANUALLY, meaning a human must put their fingers on the switch to operate it. Aux. contacts can SIGNAL the status of that switch, but cannot CONTROL it.
A magnetic starter provides a coil that can be energized and de-energized by some other electrical means be it a control system, such as your HVAC control system, or even a separate / remote manually operated switch such as push buttons or a selector switch.
In addition, you must also consider the desired operation after a power failure. On restoration of power, do you want that motor to automatically come back on? if so, is there a danger of someone being in contact with moving parts if it does? If automatic restart is not desireable, you need to use a mag. starter or an Under Voltage Trip on a manual starter. The UV Trip option however will also require a person to manually reset it after the power failure.