Two definitive words used in the Quran are Shirk and Kufr. The adjectives from these two nouns are Mushrik (one who commits shirk) and Kafir (one who commits kufr) respectively.
What exactly is shirk and what is kufr, and what is the Quranic difference between the two?
The first observation comes from the following verse, and it tells us that shirk and kufr are not the same thing:

If the two types of people were identical, they would not have been mentioned separately.
The following are words which are used in the Quran as opposites:

1- Mumin (believer) as opposed to Kafir (disbeliever)
[64:2] He is the One who created you, then among you there is the Kafir and the Mumin.

2- Mushrik (one who sets up partners with God) as opposed to Hanifan (a pure worshipper of God who accepts God’s absolute authority with no partners/monotheist). It is important here to note that to set partners with God a person must believe in God in the first place.
[6:161] Say, “My Lord has guided me to a straight path, an upright religion, the creed of Abraham. He was a hanifan and was not one of the Mushrikeen.”

• Kafir = a disbeliever, either an atheist or someone who believes in other gods besides God.
• Mushrik = someone who believes in the One God but associates partners with God in any capacity and in any of God’s exclusive rights.

The word ‘mushrik’ comes from the route word ‘ashraka’ which means to make someone a partner in something, while as the word ‘shirka’ means a partnership.

Relevant questions:

1- We note that in 4:48 God proclaims that all sins can be forgiven except shirk. Does this mean that kufr is a forgivable sin? The answer is no, and can be seen in the following verse:
[4:168] Those who have disbelieved and transgressed, God was not to forgive them, nor to guide them in any way.
By reading 4:48 together with 4:168, we note that kufr and shirk are both unforgivable sins.

2- Is someone who believes in other gods a mushrik or a kafir?
The Quran tells us that a person who believes that there are other gods besides God is a Kafir by definition. He is a kafir because he rejected the Oneness of God which is the prime attribute of God. On the other hand, a mushrik is someone who believes in God as the only god, but at the same time, associates partners with God (not as gods, but who share in God’s exclusive rights).
[12:106] The majority of those who believe in God (which includes all Muslims) do not do so without committing shirk.

3- What becomes of the deeds of the one who commits shirk or kufr?
All the deeds, of both mushrik and kafir, are nullified and count for nothing on Judgement Day:
[39:65] ……… if you ever commit shirk, your works will be nullified and you will be among the losers.
[2:217] ……. Any of you who reverts from his religion and dies as a disbeliever, for those, their works are nullified in this world and the Hereafter and these are the companions of the fire, and therein they shall remain.

4- What is the fate of one who dies as a mushrik, and is his fate different from the fate of a kafir?
Once again, we learn from the Quran that the fate of the kafir (disbeliever) and that of the mushrik (one who associates partners with God) are the same. The following verse confirms that both of them are committed to Hell:

5- Why are the Christians who believe in the Trinity called kafir (5:73) even though they believe in God?
No one can be called a believer in God without believing in the Oneness of God. A person who believes that God and Jesus are one does not believe in the true God. The one who believes in the ‘Trinity’ does not believe in the true One God. The true God is not Jesus and is not a third of a ‘Trinity’. As a result, such a person is a kafir and not a mushrik.

6- Is there really much difference between a kafir and a mushrik?
Kufr and shirk are two different symptoms of the same illness. They are two different routes that lead to the same destination; perdition.
In essence, every mushrik is necessarily one who harbours kufr as well.
The explanation of this lies in the reason why a mushrik associates partners with God. A person does so because somewhere along the line he rejects the idea of God alone.

Finally, it is worth mentioning that the Quran tells us the alarming fact that every mushrik automatically becomes a kafir as well:

The words “they disbelieve in what We have given them” gives us the reason why all mushriks are in essence kafirs as well, it is because they disbelieved in some words in the Quran which God gave them.