Istiadhah, Isti’anah, Istighathah
Isti’adhah means to say audhu (I seek refuge). It means to seek spiritual refuge, and to seek refuge in other than Allah is shirk.
“So when you recite the Qur’aan, seek refuge with Allah from the accursed Shaitaan.” (An-Nahl, 16:98)
“When the shaytaan whispers an idea to you, then seek refuge in Allah. He is the All-Hearing, the All-Knowing.” (Fusillat, 41:36)
“And, indeed, some men from among the common folk used to seek the protection of some men from among the jinn, and thus they increased the jinn in arrogance/the men in fear.” (Al-Jinn, 72:6)
Rahaqah can be fear, or it can be arrogance. If fear, then it means the jinn increased the men in their fear of the jinn. If arrogance, then the men increased the jinn in their arrogance.
In Bukhari it is mentioned that when jahiliyyah Arabs went to camp, the leader of the caravan would stand up and announce loudly that he seeks refuge in the leader in the jinn of this valley.
Isti’anah and Istighaathah
This means seeking help. Seeking help in a natural way is allowed (like calling 911 in an emergency). Seeking help in a supernatural way is unique to Allah (swt).
“You alone we ask for help.” (1:4)
“And if Allah touches you with hurt, there is none who can remove it but He; and if He intends any good for you, there is none who can repel His Favour which He causes it to reach whomsoever of His slaves He will. And He is the Oft-Forgiving, Most Merciful.” (10:107)
Both isti’aanah and istighaathah are sub-categories of du’a.