PowerShell timer/stopwatch accuracy
You have 20 1 second pauses, but you have other things going on as well. There is a loop that increments and tests a variable, and you write the elapsed time on each iteration. These extra things take time.
This still has a 20 second pause, and the elapsed time is closer to 20 seconds because there is less extra stuff that PowerShell has to do:
$elapsed = [System.Diagnostics.Stopwatch]::StartNew()
write-host "Started at $(get-date)"
sleep 20
write-host "Ended at $(get-date)"
write-host "Total Elapsed Time: $($elapsed.Elapsed.ToString())"
The question is, what are you trying to do? If you are trying to determine how long it takes a script to run, exactly, you should use the stopwatch. However, if you are trying to start a new sequence of commands after a specified period, use a [System.Timers.Timer] and register an event for the elapsed event on the timer object. Then specify the action of the registered event to what it you are trying to accomplish.