According to Hadeeths narrated from Ahlul Bayt (AS), Kursi of Allah is His Knowledge about Skies and earths and creatures which has got an outer existence, while Arsh is His Full Knowledge about everything, which is more inclusive than Kursi. There are degrees of Knowledge, in which Arsh is deeper, wider and more inclusive than Kursi, that is why we read in the Hadeeth that The Kursi is within The Arsh. In the Hadeeth from Imam Ja'far Al-Sadiq (AS): Everything created by Allah is in the Kursi except His Arsh because it is greater than be included in The Kursi.
Hadeeth of Hanan ibn Sadeer from Imam Al-Sadiq (AS) when he was asked about Arsh and Kursi, he replied: Both of them are great gates of the Unseen. Kursi is the outer gate of the Unseen and Arsh is the inner gate of the Unseen.
Kursi is limited to the skies, earth and what is between them while Arsh is unlimited.
In some narrations we read that The Kursi is the knowledge which Allah granted to His Prophets and messengers, while The Arsh is The Knowledge which no one knows but Allah.