believer and disbeliever in Islam

هُوَ الَّذِي خَلَقَكُمْ فَمِنكُمْ كَافِرٌ وَمِنكُم مُّؤْمِنٌ وَاللَّهُ بِمَا تَعْمَلُونَ بَصِيرٌ

He is the One Who created you, yet some of you are disbelievers while some are believers. And Allah is All-Seeing of what you do

―Quran 64:2

see the explanation of the verse here www.islamicstudies.info/tafheem.php?sura=64

God is our Creator. Among people some have chosen to believe in God and some has chosen to deny Him. God watches over everything man does.

another chapter says :

I do not worship what you worship, nor are you worshippers of what I worship, nor will I be a worshipper of what you worship, nor will you be worshippers of what I worship, for you is your religion and for me is my religion .

— Quran 109:2–6

commentary on -Quran 64:2 by Towards Understanding the Quran

He it is Who has created you: and among you are those that deny the Truth 5 and among you are those that believe in it. 6 Allah observes all that you do

—Quran 64:2

5. It has four meanings and all are correct in their respective places:

First, that He alone is your Creator, yet some of you deny His being the Creator and others acknowledge this truth. This meaning becomes obvious when the first and the second sentences are read together.

Second, that He Himself has created you with the nature that if you choose to adopt unbelief, you may do so, and if you choose to affirm belief, you may do so. He has not compelled you to either accept or reject the faith. Therefore, you yourselves are responsible for your adopting belief or unbelief. This meaning is confirmed by the following sentence: Allah sees whatever you do. That is, by giving you this choice He has put you to the test, and He is watching how you exercise this choice.

The third meaning is, He has created you with a sound, wholesome nature, which demands that you should all adopt the way of the faith, yet some of you adopted unbelief, which was opposed to the nature and purpose of their creation, and some of you adopted the way of the faith, which was in conformity with their nature. This theme becomes obvious when this verse is read along with (verse 30 of Surah Ar-Room) which says: Set your face sincerely and truly towards faith, and be steadfast on the nature whereupon Allah has created mankind. There can be no alteration in the nature made by Allah. This is the right and true faith. And this very theme is explained by several Ahadith in which the Prophet (peace be upon him) has repeatedly stated that every man has been created on true human nature; then polytheism and deviation befall him from outside (For further explanation, see( E.Ns 42 to 47 of the commentary of Surah Ar-Room). Here, it may he pointed out that no divine Book has ever presented the concept of man’s being a sinner by birth, which Christianity has embraced as its fundamental doctrine for 1,500 years. Recently even Catholic scholars themselves have started expressing the view that there is no basis for this doctrine in the Bible. The famous German biblical scholar Rev. Herbert Haag writes in his book, Is Original Sin in Scripture: Among the earliest Christians, at least till the 3rd century A.D. there existed no such creed that man was a sinner by birth, and when this idea started spreading among the people, the Christian scholars continued to contradict it for two centuries. At last in the 5th century A.D. St Augustine by the power of his logic made this idea a part of the fundamental beliefs of Christianity. Mankind is heir to the original sin committed by Adam, and there is no way to salvation for man except through the Atonement made by Christ.

The fourth meaning is: Only Allah brought you into existence from nonexistence: you were not, then you became. This was such a simple thing that if you had thought over it seriously and seen that life is the real blessing through which you are benefiting by the other blessings in the world, none of you would have adopted the attitude of disbelief and rebellion against your Creator. But some of you did not give it due thought or thought wrongly, and adopted the way of disbelief, and some others adopted the same way of belief and faith which was the very demand of correct thinking.

6. In this sentence seeing does not merely mean to see, but it automatically gives the meaning that man will be rewarded or punished according to his actions and deeds. It is just like a master’s taking a person into service and then telling him: I shall see how you perform your duties, which implies: If you perform your duties well, I shall reward you fully; otherwise I shall call you to account for your negligence.