The remote running means that the script or program is present on another computer on the network and that it must be run remotely using his network path. For example: \\POINTDEV\MySharedScript\script.bat.
In this case, the program to be run must be in a shared directory available from each target computer and the execution account must have access permissions to the shared directory.
In the case of remote running, each computer runs the executable file on the remote machine. Network traffic is mainly during the execution phase. It is therefore recommended to limit the number of concurrent executions in the case of a remote execution of a large file on a large number of computers to reduce network traffic.
If you want to run a program already present on all target computers, you must use the remote execution. So, if you select c:\script.bat as executable file and you do not check "Local Running", then the distribution agent present on each target computer will locally run the file c:\script.bat.
The local running means that the script or program is copied to all target computers in the %windir%\IDispatchAgent\Scripts folder then executed and removed on completion.
In the case of a local running, the distribution server copy files to each target. Network traffic is mainly during the installation phase. It is therefore recommended to limit the number of simultaneous installations in the case of the local running of a large file on a large number of computers to reduce network traffic.