When you ask, 'what makes a light soft,' you're really asking 'what makes soft shadows?' In other words, when we talk about soft light, we're actually referring to the shadows.
There is just one thing that will affect the softness of the shadows from a light. It is a light's relative size that affects its softness.
Light doesn't bend - it only travels in a straight line. The thing that soften shadows is that part of the light can 'see' the dark side of the whatever you're illuminating.
So, if you're buying a little white cap to go on the end of your flash, you're not making it more soft.
These caps are dumb. They shouldn't be sold. It's misleading. Technically, this is a diffuser. It's a diffuser in that it spreads the light in different directions. The possible benefit is if you're in a small white room where the light is going to bounce off of walls and fill in the shadows.
If you buy a diffuser that actually enlarges the size of the flash significantly, you will make the light softer. I use a 24" expandable soft box. It has a baffle inside that diffuses the light before the outer scrim - which diffuses the light again.
This type of diffuser significantly increases the size of the flash. It allows part of the light to 'see' around the subject's facial features - which softens the shadows. Again, it's a light's size that makes the shadows softer. If something claims to 'bend' light, it's not true.