Showing past events in calendar only

Actually, I want the calendar to show all events and the event lists only show upcoming events.

Ok, so just leave the default settings to hide past events and use a filter hook to show past events in calendar only:

// show past events in the calendar
function em_get_full_calendar_events_args( $args ) {
	$args['event_show_past_events'] = true;
	return $args;
}
add_filter( 'em_get_full_calendar_events_args', 'df_em_get_full_calendar_events_args' );