In general, the adjust like a spring stretches the entire part along an axis.
The other version I have not had much luck with trying to use and resorted to use planes to control the size of parts.
Just to note that adjust to fit can be determined by angle as well as distance. I use angle often for hinges. Also use distance for rod extension on cylinders.
Here is a short video:
The main difference is that you can move underconstrained parts at "Adjust like a spring" and "spring" will be updated while you can not move directly at others, but you may add assy relationships... The second is very similar to Inventors' adaptive part...