As per documentation, if your script uses argument0 and argument1, you pass them to live_call (otherwise live-reloaded code would show an error due to not knowing their values); live_call_ext is used for scripts that take a varying number of arguments.
live_defcall/live_defcall_ext are used if you need the system to return a specific value if your updated code has compilation/runtime issues - e.g. if you are making changes to a script that returns a string, you might want it to still return some blank/"error" string even if you temporarily mess up something (to avoid non-"live" code throwing an error and closing the game).