The differences are:
1. In the Target Downside Deviation calculation,
the deviations of Xi from the user selectable
target return are measured, whereas in the
Standard Deviation calculation, the deviations
of Xi from the average of all Xi is measured.
2. In the Target Downside Deviation calculation,
all Xi above the target return are set to
zero, but these zeros are still included in the summation.
The calculation for Standard Deviation has
no Min() function.
Standard deviation is a measure of dispersion
of data around its mean, both above and below.
Target Downside Deviation is a measure of dispersion
of data below some user selectable target
return with all above target returns treated as
underperformance of zero. Big difference.