Are Islam and Imaan the same thing?
For each of the two there is a specific meaning. Islam is defined as the apparent actions such as the Two Testimonies of Islam and the prayer, and Imaan defined as the internal actions of belief, such as reliance, fear, love, hope and reverence.

From the evidence for this:
-      The Statement of Allah the Exalted, The Muslim men and women, and the believing men and women… al-Ahzaab: 35 Ash-Shawkaanee said, “By His saying (The Muslim men), He, Glorified be He, started with the mention of Islam as simply the entering into the religion, and the compliance towards it by way of action, as was established in the authentic hadeeth that the Prophet ? when he was asked by Jibreel regarding Islam, he said, “It is that you testify that there is no deity worthy of worship except Allah, and you establish the prayer, give the obligatory alms, make pilgrimage to the House, and that you fast Ramadan.” [185] Reported by al-Bukhaaree (50), and Muslim (9) at length with slight variations from the hadeeth of Abu Hurayrah (may Allah be pleased with him). … then He mentioned (the believing men and women) and they are those who believe in Allah, His angels, His books, His Messengers, and in the Decree, both its good and bad, as was established in the authentic reports from the Messenger of Allah ?. [186] Reported by al-Bukhaaree (50), and Muslim (10) at length with slight variations from the hadeeth of Abu Hurayrah (may Allah be pleased with him). ” [187] “Tafseer as-Samarqandee” (3/61)

-      The Statement of Allah the Exalted, The Nomad of Arabs say, “We have believed.” Say “You have not yet believed, rather say you have submitted, and Imaan has not yet entered into your hearts” al-Hujuraat: 14 Ibn Katheer said, “The Exalted is rejecting the claim of the Bedouin Arabs who when they first entered into Islam, claimed that they were at the station of Imaan, whereas Imaan had not yet been established in their hearts, (The Bedouin Arabs say “We have believed.” Say “You have not yet believed, rather say you have submitted, and Imaan has not yet entered into your hearts”) and what we benefit from this noble ayah, is that Imaan is more specific than Islam, as is the opinion of the people of Sunnah. It is also indicated by the hadeeth of Jibreel – may Allah’s salutations be upon him – when he asked about Islam, then about Imaan, then about Ihsan, in doing so going from the most general, to the specific, to the most specific… So, this indicates that these aforementioned Bedouin Arabs in this ayah were not hypocrites, rather they are Muslims who have yet to establish Imaan in their hearts, yet they claimed for themselves a station that they were yet to reach. Thus, they were disciplined for that, and this is the view of Ibn ‘Abbas, Ibraaheem an-Nakh’iee, Qataadah, and what was chosen by Ibn Jareer.” [188] “Tafseer Ibn Katheer” (7/389) Ibn ‘‘Uthaymeen said, “In conclusion; Islam in a general sense, means the religion as a whole, and Imaan is included within it. Yet, if it is partnered with Imaan, then Islam is understood as the apparent actions, from the speech of the tongue and the actions of the limbs, and Imaan is understood the internal actions, from the beliefs of the heart and its actions.” [189] “Majmoo’ Fataawa wa Rasa’il al- ‘‘Uthaymeen” (1/49)

The necessary connection between Imaan and Islam
This is based upon the understanding that there is a difference between Imaan and Islam, wherein there is no Islam for the one who has no Imaan, and there is no Imaan for the one who has no Islam, for a Muslim cannot be void of any Imaan by which their Islam is valid, and a believer cannot be void of any Islam by which they realise their Imaan, due to what there is between the outward and inward of association and necessary connection. Ibn Abi Shaybah said, “There can be no Islam without Imaan, nor Imaan without Islam.” [190] “Ta’theem Qadr as-Salaah” (2/528) Aboo Taalib al-Makkee said, “The example of Islam and Imaan is like the example of the two parts of the Two Testimonies of Islam in their meaning and rulings. The testification regarding the Messenger is not the same as the testification of Allah’s oneness, for they appear as two separate things, but one is connected to the other, so they are as one thing: there being no Imaan for the one with no Islam, and no Islam for the one with no Imaan. For a Muslim cannot be void of any Imaan by which their Islam is valid, likewise there must be within the Muslim Imaan by which their Imaan is realised, since Allah, Glorified be He, has made Imaan a requisite for good deeds, and made righteous deeds a condition of Imaan.” [191] “Qoot al-Quloob” (2/216)

The fruit of the separation between Islam and Imaan
The fruits of the opinion that Imaan and Islam are separate are:
1.   Showing Imaan to be degrees, like how the Prophet defined it, ?.
2.   That Imaan is more virtuous than Islam, in the same way that Ihsan is more virtuous than Imaan.
3.   That entering into paradise is connected to Imaan and Islam. [192] “Qawaa’id fi Bayan Haqiqat al-Imaan ‘ind Ahl as-Sunnah wal-Jamaa’ah” – ‘Adel ash-Shaykhaanee (p.296)