All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
The term Kufr and Shirk can be interchangeable. Shirk could refer to associating others in worship to Allaah, and Kufr could refer to what is greater than that to include Shirk and disbelieving in one of the pillars of Islam, or other acts in the heart. If these two terms are mentioned in one context, their meaning is different, but if only one term is mentioned, then it includes the meaning of the other one.
Imaam An-Nawawi commented on the explanation of the book of Imaam Muslim regarding the narration of the Prophet : "The line of demarcation between a man and Shirk or Kufr is abandoning the prayer." [Muslim] He said: "Shirk and Kufr could be mentioned to mean one thing, which is disbelief in Allaah. But their meaning could differ, Shirk could mean worshipping idols or other creatures while acknowledging the existence of Allaah, like the Kufar of Quraysh, so the term Kufr is more general than Shirk."
Therefore Kufr is of two kinds:
1) Major Kufr that takes one out of the fold of Islam.
2) Minor Kufr that does not take one out of the fold of Islam.
Shirk is also of two kinds:
1) Major Shirk that takes one out of the fold of Islam.
2) Minor Shirk that does not take one out of the fold of Islam, like slight showing off.
The kinds of Kufr are due to four reasons:
A) Kufr resulting from ignorance or denial.
B) Kufr resulting from rejection of faith.
C) Kufr resulting from stubbornness and arrogance.
D) Kufr resulting from hypocrisy.
If a Muslim commits Major Kufr or Major Shirk, we have to establish evidence against him, and if after this he still does not want to change his opinion then he is a Kaafir who will eternally dwell in hellfire. Allaah says (which means): {Indeed, he who associates others with Allaah - Allaah has forbidden him
For more information about Shirk and its types, please refer to Fataawa: 82456 and 82858.
Allaah knows best.