If you would like to know general knowledge about Bootstrap and Simulation in JMP, the link (2) and (3) are more relevant. Link (1) is a more advance topic, and specific to DOE.
William Meeker is one of the speakers of (2) and (3). You may want to check out Chapter 9 of his book "Statistical Methods for Reliability Data", 2nd. ed. If you only have access to its first edition, it is also Chapter 9 that you should check out. The very detailed descriptions are documented there. Many of us learned the techniques there. But I am sure there are other references. Meeker's materials cover both the general concepts of the techniques, and special applications of reliability analysis. If the reliability analysis part is irrelevant, you may safely skip.
If I would summarize what are in the book, together with what Mark explained, the following is my stab.
The steps of "Bootstrap", AKA "nonparametric bootstrap", include:
- sample from your data
- do something
- calculate the quantity of your interest, collect quantity
- repeat.
The steps of "Simulate", AKA "parametric bootstrap", include:
- starts with a model with some known parameters, simulate a sample from it
- do something
- calculate the quantity of your interest, collect the quantity
- repeat.
As you have mentioned, the purpose is to get "confidence interval". Which to choose? That depends on your task. I cannot speak to the task that you have described. But look at link (2) and (3), link (2) and majority part of (3) are related to applications of the "nonparametric bootstrap" (or Bootstrap), because the task is to better quantify confidence interval of estimates, for which large sample approximation is not the most effect approach in the context. Now look at when "parametric bootstrap" (or Simulate) is used in link (3), that is for power calculation. What is power calculation? For that kind of calculation, one must know the truth, so when a decision is made by an method, one must know whether the decision on a hypothesis test is correct or not. Then one can sweep the conclusion into the correct quadrant in the table of Type I and type II errors . How can one be sure about the truth? Just start with the truth. That is when "parametric bootstrap" is more appropriate.
The bootstrap methods are versatile technologies, I am sure what I described is a tip of the iceberg. But what Mark said summarizes the difference: they have different starting points.
For your specific task, I have one question, when you did the Simulate, how did you come up with the formula column? Is it the truth that you know?