What is the difference between a soft starter and a VFD?

A VFD is always a soft starter in addition to being a speed/torque control device. While a soft starter is equipment used only to reduce or limit the starting current. There are many soft starting methods like using grid rotor resistance, auto transformer, thyristor bases soft starter and finally even optimally designed VFD being used just as starter.

A soft starter is just that. It allows the motor to ramp up to full speed and maybe ramp down to a stop. An AC drive is needed to control speed and usually includes additional features such as multiple speed settings and S curve deceleration. Consider the needs of your application and the benefits of additional flexibility versus the difference in cost. For smaller motors, an AC drive will often provide a lot of additional flexibility and future proofing for a small additional cost. But, this is not always the case so it really depends on the details of you application and budget.

A soft starter is a starter configured such that it will ramp up the voltage/current allowing the motor to start off slowly and pick up speed without the typical inrush.

The AC drive is as variable frequency drive which allows the motor to be operated over a range of speed in a controlled manner, and since you can control the speed of the motor it could have the effect of a soft starter.

AC drive is obviously more costly, it can have two acceleration sessions with different ramping rates (from still to minimum speed with and from min speed to target speed), some delay is added prior to start.

Soft Starter is like a 2 stage starter like half voltage when a pump starts rolling a timer runs down then full voltage full speed, AC drive as is description variable voltage has capacitors to vary the voltages.

If an application and say pump at full volume is required then you can go with a Soft Starter (also reduces line voltage inrush current demand when starting), If application requires you to control and able to adjust for a volume demand then go with an AC drive.

"But" you can operate an AC drive at a fixed speed and have the ability control the startup ramp rate and also ramp rate as it shuts down, I haven't had any soft starters ramp a motor down in reverse order as startup just cuts off the voltage when shutting down.