What is the purposes of different operator in script task output tab's custom output

Hope this helps! 

https://docs.appian.com/suite/help/25.3/Process_Node_and_Smart_Service_Properties.html#custom-outputs

They're use-case dependent, and they pretty much do what they say.

"Stored As" = the output of the expression in the expression box is stored into the selected PV, overwriting it.

"Appended to" = the output is added as a new entry at the end of the array currently stored in the PV (or becomes the first entry if it's empty).

"Stored at Index" allows you to take an established array and overwrite a particular index (i.e. list item number) with the evaluated expression value.

Interestingly, when the output PV is set to an Integer (and possibly also a decimal, i did not test this), you get some more options:

These, of course, overwrite the PV value with the result of applying the expression's output to the pv's current value considering the selected operator.  I've never really used these, though, as it's easier to control (and understand) the resulting output by simply doing the operation you want in the expression editor box.  AFAIK all of these can be simply done by using different expression operations, meaning we pretty much only ever (routinely) need "stored as".

The "is appended to list" option in output appends the result to a list variable instead of overwriting it, unlike "is stored as" which replaces the variable's value.
It is used to accumulate multiple outputs into one list.