Active=only stops for summons/equivalents.
Recomended=atbs gauges stop filling while attacks/magic are actually happening.
Wait=ATBs also stop while spell/item/target selection menus open.
It has NEVER stopped when the root menu was open ever.
In all three settings, as near as I can tell, any ENEMY who's gauge (that you can't see) fills goes instantly, or after the current attack animation finishes if on active, while party members go in the order they filled. limit breaks are sort of an exception, as even if you have a party member's gauge that filled while an enemy was taking a turn, if the enemy's attack caused a limit gauge to fill, that character will be lined up for next turn as soon as the limit break is selected and targeted.
The practical result is that on Active if you have any menu open including root, ALL player turns are paused regardless of player ATB gauges, and ALL enemy turns that are ready can cut ahead in line until you lock in a player action. On Recommended the enemy gauges fill up slower because they are paused during attacks. On wait, opening a submenu stops the enemies from adding to their gauge.