Without getting into the mathematics of the situation which is covered by others with graphs and equations, let me try to clarify the difference between these two different aspects of the lighting.

Quantity and quality.

The quantity or the amount of light is determined by how far the light travels. All other things being equal, the shorter the distance the greater the amount of light falls onto the subject. The inverse-square law refers to this aspect. The formulas and graphs are an attempt to quantify the change of intensity with the distance.

The quality of the light is determined by the relative size of the source. Generally, the bigger, the softer. Some refer to soft light as "wrapping around" the subject. The transition from highlight to shadow of a soft source is gradual and smooth. As the source diameter diminishes to a spot the shadows "harden" and cast sharp, abrupt shadows. As a source gets further from the subject, its diameter relative to the subject diminishes too.

TIP:
The f/ #s on the barrel of a lens can be used to judge the depth of light fall-off - without a calculator - due to the application of the inverse-square law.
From 2.8 to 4 feet, the light will fall off 1 stop.
From 4 to 5.6 feet, the light will fall off another stop
From 5.6 to 8 feet, the light will fall off another stop
From 8 feet to 11 feet, another stop, and so on.

Using this TIP, you can see that putting a model about 6 feet from the source, gives the photographer a full 2-1/2 foot-deep zone of light that has less than a stop fall off. This is well within the lighting ratio for, and range of, flattering portrait light. (This is an application of the Inverse-Square Law)

Suppose the subject was a piece of equipment that was 3 feet wide. Placing the subject 8 feet from the source ensures that from the closest point to the furthest point of the equipment is within one stop—well within the acceptable lighting ratios for product photography printed brochures. (This is another example of the Inverse-Square Law)