AFAIK the iron man modes only differ in the possibilities where the player can save the game. All three modes have in common that you can't save during turn based combat.

"Extreme" means that you can only save at a certain time of day. Check "EXTREME_IRON_MAN_SAVING_TIME_NOTIFICATION" and "EXTREME_IRON_MAN_SAVING_HOUR" in Ja2_Options.ini.

Standard "Iron Man" mode means that you can't save the game as long as there are enemies in the current sector no matter if realtime or turnbased combat mode is active.

"Soft" means you can save at any time even if there are enemies in the current sector as long as there is no turn based combat going on.