That calculator is not mine, so I can only guess at how it works. I have been able to verify a few of the data point so I think it is correct. I am quite confident it is calculating CAGR, not some kind of average.

Some other things, I think it is calculating using every months data available. Maybe the other calculator uses data at start of year. As maizeman identified it is using data back to 1871 which makes a difference. There were some brutal periods in there, I think 1906-1921 had negative real returns for instance.

If you want to check their numbers go to their standard return calculator, if you look at some of the brutal start periods, 1929 or 1906 you should be able to find some of the numbers you see.

Also, the worst 20 year period it has is -.2%. I don't know exactly when that was but I found a 19 year period from august 1901 to august 1920 that had -0.1% (yes negative one tenth of a percent CAGR).