Soft starter is an AC motor controller that ramps the motor up to full speed slowly and gently with less starting current over a longer (albeit limited) time, but it always results in full speed operation of the motor.
Breaker is an on-off device that protects electrical circuits from short circuits and possibly over current conditions, depending on the type of breaker that you select.
VFD is an AC motor controller that does everything that a soft starter does, but also facilitates operation at any speed between zero and maximum for the motor, for an indefinite amount of time.

A Soft Starter is a power electronics variant on a reduced voltage starter. The key difference is the soft start is gated on and ramped up in voltage until you reach full speed, at which point it can be bypassed to save the energy loss in the power electronics; it thus can be described as a 'bumpless' transition to full speed since you really don't get a momentary inrush 'bump' as the standard reactor, auto-transformer or delta-wye starter gives when it is transitioning from start to run configuration.

The difference between line starting a motor and ramp starting the motor with a frequency inverter is that the motor/load does not pull the 6-7 times rated current of the motor, because the motor winding are not saturated with the full EMF produced to get the motor to synchronous speed it is ramped to it. If you are not trying to control the motors speed from process control then a soft start will serve the same purpose. The inverter main purpose is to control the V/F of the motor.

1) No surge current, during motor starts, the soft starter increase the thyristor conduction angle gradually to make the motor current rises from zero to the set value in linear.
2) Constant current start, soft starters can be applied current closed-loop control to make the motor current keep constant during starting to ensure smooth start.
3) Adjusting optimized starting current in stepless free according to the load characteristic and the power grid protection characteristic.