The Difference between the `Arsh the Kursi
Question

What is the difference between the `Arsh and the Kursi of Allah?
Praise be to Allah.Difference Between the `Arsh and the Kursi in Islam
The Kursi is the footstool of the Most Merciful, according to the most correct of the scholarly opinions on the matter. The `Arsh (Throne) is the greatest of all things that Allah has created, over which our Lord rose in a manner that befits His Majesty . It has pillars and is carried by bearers who are angels of immense size.
Evidence from Hadith and Scholarly Views on the Arsh and Kursi
The evidence for the above is given below, along with the comments of some of the scholars.
It was narrated that Ibn Mas`ud said: Between the first heaven and the one above it is (a distance of) five hundred years. Between each of the heavens is (a distance of) five hundred years. Between the seventh heaven and the Kursi is (a distance of) five hundred years. Between the Kursi and the water is (a distance of) five hundred years, and the Throne is above the water . Allah is above the Throne, and nothing whatsoever of your deeds is hidden from Him. (Narrated by Ibn Khuzaymah in At-Tawhid, p. 105 and Al-Bayhaqi in Al-Asma’ was-Sifat, p. 401).
This report was classed as authentic by Ibn Al-Qayyim in Ijtima` Al-Juyush Al-Islamiyah (p. 100) and Adh-Dhahabi in Al-`Ulu (p. 64).
Shaykh Ibn `Uthaymin (may Allah have mercy on him) said:
This Hadith stops at Ibn Mas`ud (it is Mawquf), but this is one of the matters concerning which there is no room for personal opinion, so it comes under the heading of Marfu` [Hadith whose chain of narration goes back to the Prophet (peace and blessings of Allah be upon him)], because Ibn Mas`ud is not known to have taken anything from the Isra’iliyyat [reports derived from Jewish sources]. (Al-Qawl Al-Mufid Sharh Kitab At-Tawhid, 3/379)
Imam Muhammad ibn `Abd Al-Wahhab (may Allah have mercy on him) said, in the list of points noted from this Hadith:

The great size of the Kursi in relation to the heavens.
The great size of the Throne in relation to the Kursi.
That the Throne is something other than the Kursi and the water. (Sharh Kitab At-Tawhid, p. 667, 668).

The Throne of the Most Merciful is the greatest and most vast thing in His creation.
Allah says (interpretation of the meaning):
{So Exalted be Allah, the True King: La ilaha illa Huwa (none has the right to be worshipped but He), the Lord of the Supreme Throne!} [Al-Mu’minun 23:116]
{and He is the Lord of the Mighty Throne} [At-Tawbah 9:129]
{Owner of the Throne, the Glorious} [Al-Buruj 85:15]
Al-Qurtubi (may Allah have mercy on him) said:   The Throne is mentioned on its own because it is the greatest thing that Allah has created; everything else is also included in this.   (End quote from Tafsir Al-Qurtubi, 8/302, 303)
Ibn Kathir (may Allah have mercy on him) said:
{and He is the Lord of the Mighty Throne} [At-Tawbah 9:129 – interpretation of the meaning] means, He is the Sovereign and Creator of all things, because He is the Lord of the Mighty Throne which is the roof of creation. All created things, the heavens and the earth and all that is in them and in between them are beneath the Throne of Allah and are subject to His power. His knowledge encompasses all things and His power controls all things, and He is Watcher over all things.   (End quote from Tafsir Ibn Kathir, 2/405)
And he said (may Allah have mercy on him):
{Owner of the Throne} [Al-Buruj 85:15 – interpretation of the meaning] means, the Master of the Mighty Throne which is above all created things . “The Glorious” – there are two readings of this word (Al-Majid). If it is nominative (Al-Majidu) it is an adjective referring to the Lord, may He be glorified, and if it is genitive (Al-Majidi), it is an adjective referring to the Throne. Both meanings are correct.   (End quote from Tafsir Ibn Kathir, 4/474)
Majid means vast and mighty in power.
It was narrated from Abu Sa`id (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) said: “The people will fall unconscious on the Day of Resurrection; I will be the first to regain consciousness, and Musa will be there, holding on to one of the pillars of the Throne. I do not know whether he woke up before me or if he was exempted because he had fallen unconscious at the Mount of Sinai.” (Narrated by Al-Bukhari, 3217)
The Throne has bearers who carry it.
Allah says (interpretation of the meaning):
{Those (angels) who bear the Throne (of Allah) and those around it glorify the praises of their Lord, and believe in Him, and ask forgiveness for those who believe (in the Oneness of Allah) (saying): ‘Our Lord! You comprehend all things in mercy and knowledge, so forgive those who repent and follow Your way, and save them from the torment of the blazing Fire!’} [Ghafir 40:7]
They are of immense size:
It was narrated from Jabir ibn `Abdullah that the Messenger of Allah (peace and blessings of Allah be upon him) said:
{I have been granted permission to speak about one of the angels of Allah, one of the bearers of the Throne. The space between his earlobes and his shoulders is the distance of seven hundred years’ travelling.} (Narrated by Abu Dawud, 4727)
Al-Hafidh Ibn Hajar (may Allah have mercy on him) said concerning this Hadith: its chain of narration meets the conditions of being authentic. (End quote from Fat-h Al-Bari, 8/665)
The Throne is above the Kursi, and is above all of creation. Ibn Al-Qayyim (may Allah have mercy on him) said:
If Allah is separate from His creation, then either He is encompassing them or He is not. If He is encompassing them, then He must be above them, because that which encompasses must necessarily be above that which is encompassed. Hence because the heavens encompass the earth, they must be above it, and because the Kursi encompasses the heavens, it must be above them, and because the Throne encompasses the Kursi, it must be above it. Whatever encompasses all of that must necessarily be above it. This does not imply that there is physical contact with anything that He encompasses; neither is there any similarity or resemblance between Him and that which He encompasses. (End quote from As-Sawa`iq Al-Mursalah, 4/1308)
The Throne is neither Sovereignty (Al-Mulk) nor the Kursi.
Ibn Abu Al-`Izz Al-Hanafi (may Allah have mercy on him) said:
What would those who distort the word of Allah and say that the Throne is an expression referring to Al-Mulk or sovereignty say about the following verse? –
{…and eight angels will, that Day, bear the Throne of your Lord above them} [Al-Haqqah 69:17 – interpretation of the meaning]
{…and His Throne was on the water…} [Hud 11:7 – interpretation of the meaning]
Will they say that eight angels will, that Day, bear the Sovereignty of Allah, and that His Sovereignty was on the water? Will Musa be holding on to one of the pillars of Allah’s sovereignty? Can any same person who knows what he is saying utter such things?
Concerning the Kursi, Allah says (interpretation of the meaning):
{His Kursi extends over the heavens and the earth.} [Al-Baqarah 2:255]
It was said that this is the Throne, but the correct view is that it is something else. This was transmitted from Ibn ‘Abbas (may Allah be pleased with him) and others. Ibn Abu Shaybah narrated in Sifat Al-`Arsh, and Al-Hakim narrated in his Mustadrak that [the following  report] meets the conditions of the two Shaykhs [Al-Bukhari and Muslim] although they did not narrate it: (it was reported from) from Sa`id ibn Jubayr that Ibn ‘Abbas (may Allah be pleased with him) said, concerning the ayah (interpretation of the meaning):
{His Kursi extends over the heavens and the earth.} [Al-Baqarah 2:255]:
The Kursi is the footstool, and no one can comprehend how vast the Throne is except Allah.
This was transmitted as a Marfu` report (attributed to the Prophet (peace and blessings of Allah be upon him)), but the correct view is that it is Mawquf, stopping at Ibn `Abbas…
Abu Dharr (may Allah be pleased with him) said: I heard the Messenger of Allah (peace and blessings of Allah be upon him) say: “The Kursi in relation to the Throne is like an iron ring thrown out into empty land.”
And, as one of the Salaf said, before the Throne it is like a step.  (End quote from Sharh Al-`Aqidah At-Tahhawiyyah, p. 312-313)
Shaykh Ibn `Uthaymin (may Allah have mercy on him) said:
There are those who say that the Kursi is the Throne because of the Hadith, “Allah will set up His Kursi on the Day of Resurrection.” They think that the Kursi is the Throne.
Similarly, some people claim that the Kursi is Allah’s knowledge, and say that the verse (interpretation of the meaning):
{His Kursi extends over the heavens and the earth.} [Al-Baqarah 2:255] refers to His Knowledge.
The correct view is that the Kursi is a footstool, and the Throne is that which the Most Merciful rose above (Istiwa’). And knowledge is the attribute of the knowledgeable one by means of which he understands that which he knows. (End quote from Al-Qawl Al-Mufid Sharh Kitab At-Tawhid, 3/393, 394)
And Allah knows best.