Hi Annet,
In my observation, this difference is more often ignored than used.
One scales the axis, the other one moves points to scale. Each has its downsides and advantages. If you like to scale a whole scene, use the scale parameters. Tip, if there is any animation of a child object, all axis of the parent must be scaled the same.
A quick demo of the differences, not as a replacement for the manual, but it shows the core concepts. One problem I have not shown. When the points (Structure Manager) are moved to scale, they can be scaled to zero. There is later on no way back from that. In animation, that is sometimes wanted. With the Object tool, that is possible, as it leaves the point values where they are.
Clip:
https://www.amazon.com/clouddrive/share/c7EamdkIAnuz5ppRAspcxga8jZuCaM0RMSZ2CRWf6OE
Cheers