Islām is a way of life. Another definition of Islām is inqiyād ẓāhirī, which is the manifestation of taṣdīq through actions.
Imān can be thought of as taṣdīq bi al-qalb (affirmation in the heart), and Islām as a’māl (actions).
It seems as though the two words, Islām and Imān are different in meaning. For example in the following ayah:
قَالَتِ الْأَعْرَابُ آمَنَّا ۖ قُل لَّمْ تُؤْمِنُوا وَلَٰكِن قُولُوا أَسْلَمْنَا وَلَمَّا يَدْخُلِ الْإِيمَانُ فِي قُلُوبِكُمْ ۖ وَإِن تُطِيعُوا اللَّهَ وَرَسُولَهُ لَا يَلِتْكُم مِّنْ أَعْمَالِكُمْ شَيْئًا ۚ إِنَّ اللَّهَ غَفُورٌ رَّحِيمٌ
The bedouins say, “We have believed.” Say, “You have not [yet] believed; but say [instead], ‘We have submitted,’ for faith has not yet entered your hearts. And if you obey Allah and His Messenger, He will not deprive you from your deeds of anything. Indeed, Allah is Forgiving and Merciful.” Quran 49:14
Even though, in essence they may be different, in sharī’ah to be beneficial, from a certain perspective they are closely bonded together. For example, for Imān to be considered then part of Islām is needed ie. in order for a person to be considered to have Imān, then there needs to be some manifestation of this Imān through their Islām (actions).
Iqrār (affirmation) is a compulsory tenet of Imān, and Islām is a condition of Imān. Two things which are different in essence can be dependent on each other. For example, take the sun and daytime, although they are two different things, you cannot get daytime without the sun.
The importance of Iqrār bi al-lisān, in order for Imān to be accepted
For the ruling of Muslims to apply in this world, Iqrār bi al-lisān (affirmation with the tongue) is a condition by consensus of the scholars ie. if a person did taṣdīq but did not do iqrār then the ruling of Muslims in this world will not apply.
