Sometimes the answers to broad questions like this are best answered by doing s little searching on your own. For instance I copied your the stone column part of your title and then did a Google search and many explanations came up I'm sure if you did the same for pile driving you also would find many.
Each one is different with different methodologies to do the same thing, improve the properties of a subgrade. And your question has so many nuances and levels, it's hard to answer.
If you want a contractor's point of view, call a contractor. Hayward Baker is real good.