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What kind of standard error do Calc and Charts use for error bars?

I tried to find in the documentation what is the calculation used to ad "standard error" error bars on a chart, but could not find any explanation.

I tried to create a chart with two versions:

  1. the automatic standard error error bars from the "Insert > error bars" menu
  2. the same but with my own calculated values for standard error of the mean, using the formula Std err = Std dev of the sample / square root of the sample size.

Here is the spreadsheet.

Could anyone explain to me why the resulting error bars are different from one to another?