I can't answer for Intercst - but he is the author of the spreadsheet, so he certainly knows how it works.
Now, about why they differ:
They both used the same data when written, but they aren't the same program. In writing Firecalc, I worked from scratch in developing the algorithms, rather than trying to reverse-engineer Intercst's spreadsheet. There are probably a few differences in such things as when the expenses are deducted from the portfolio (before or after inflation is applied that year?), for example.
In addition, there were some deliberate differences, such as applying the first withdrawal immediately upon retirement rather than 364 days later..Also, I felt that the bad years of the late 60s were being left out of too many analyses for the 40 year runs many people were doing, so my analysis includes partial cycles, such as 1969-2001, when Intercst's spreadsheet stopped the analysis at 1961 for the 40 year runs. This lets me catch more failures for those years, but also changes the numbers used in the success rate equation.
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