Fahm (فہم) is a faculty or process of mind which enables a person to grasp the true meaning of a word/concept or real substance of a case, e.g.,

فَفَهَّمْنَاهَا سُلَيْمَانَ

And We gave understanding of the case to Solomon

[Al-Quran Surah 21: Verse 79]

Shu’oor (شعور) is a faculty or process of mind which enables a person to perceive subtle realities or grasp the minute particulars of a subject, e.g.,

وَلَا تَقُولُوا لِمَن يُقْتَلُ فِي سَبِيلِ اللَّـهِ أَمْوَاتٌ ۚ بَلْ أَحْيَاءٌ وَلَـٰكِن لَّا تَشْعُرُونَ

And do not say about those who are killed in the way of Allah, “They are dead.” Rather, they are alive, but you perceive [it] not.

[Al-Quran Surah 2: Verse 154]

Fiqh (فقہ) is a faculty or process of mind which enables a person to grasp true nature of something; or to deduce or draw inferences about specific cases, in the light of general principles or laws, e.g.,

تُسَبِّحُ لَهُ السَّمَاوَاتُ السَّبْعُ وَالْأَرْضُ وَمَن فِيهِنَّ ۚ وَإِن مِّن شَيْءٍ إِلَّا يُسَبِّحُ بِحَمْدِهِ وَلَـٰكِن لَّا تَفْقَهُونَ تَسْبِيحَهُمْ ۗ إِنَّهُ كَانَ حَلِيمًا غَفُورًا

The seven heavens and the earth and whatever is in them exalt Him. And there is not a thing except that it exalts [Allah] by His praise, but you do not understand [the nature of] their exalting. Indeed, He is ever Forbearing and Forgiving.

[Al-Quran Surah 17: Verse 44]

Aql (عقل) is a faculty of mind which enables a person to grasp the reasonableness or propriety of something; and withholds or restrains him from doing anything that is not suitable or befitting, e.g.,

إِنَّ شَرَّ الدَّوَابِّ عِندَ اللَّـهِ الصُّمُّ الْبُكْمُ الَّذِينَ لَا يَعْقِلُونَ

Indeed, the worst of living creatures in the sight of Allah are the deaf and dumb who do not use reason.

[Al-Quran Surah 8: Verse 22]