The Quran uses the term Muslims to all those that voluntarily submit to the divine will, whether that will manifested through Abraham, Moses, Jesus or Muhammad. Submission to the Divine Will, willingly or not, is according to the Quran, an observable reality in the universe down to our inner selves, since the origin of things 3:83-5,13:15,19:88-95,22:18 until all are commanded and made to disintegrate and resurrect 84:2.
That submission however is different in the spiritual realm.
The creatures, including the humans, endowed with a spirituality, are to volontarily choose submission to the divine will. It will never be enforced upon them. No other din/way is acceptable to Allah, other than volontary self-submission, the meaning of Islam 3:19,2:127-130 because it is the natural fabric of the universe. Those who choose not to surrender totally to God or humbly and freely comply with His order of life, appear out of place in this design
3:83"Do they seek a religion other than God’s, when every soul in the heavens and the earth has submitted to Him, willingly or by compulsion, and to Him they shall all return?"
Islam and its derivatives (muslim, aslama) are used throughout the Quran to denote one's adoption of the divine will with his heart and soul, symbolized by "the face" in classical Arabic
2:112"whoever submits his face (aslama wajhahu) to Allah and he is the doer of good (to others)..".
To further corroborate, those claiming to adhere to the Quran are told to further
2:208"enter into the silm/the volontary self-surrender".
Being a "Muslim" is thus on a higher level that mere acceptance of the Quran and Islam, it transcends the simple label as understood nowadays. What it really entails is subordinating all aspects of one's life to the divine will. With the revelation of the Quran none may be labelled Muslim except those who adhere to it in faith and deeds. This isnt because of following the Quran per se, but because it is the final manifestation of the divine will. Prior to it, every individual that followed the latest manifestation of the divine will through a prophet of the time, could equally be labelled Muslim. With the Quran, the path to voluntary self-servitude to the divine will has been defined is such a clear way, that no compulsion is necessary for it to be adopted by a reasonable person 2:256,18:29. Through it, the divine will manifests in its purest form.
That is why people of all ages and backgrounds have been entering into its fold like waves upon waves 110:1-3. There was no need to forcefully spread it.
Any appellation that carries a connotation other than the one conveyed through "Muslim" and "Islam" is nothing but a distortion of this simple originality taught from Adam to Abraham, Moses, Jesus and down to Muhammad. When concluding in sura anbiya the stories of some of the most eminent prophets and pious personalities, the passage ends with a statement that these people that preceded, including the newly established nation of the last prophet are in fact a single nation with the same ultimate aims, despite the apparent disconnect between those that claim spiritual affiliation to them 21:92-3.
No prophet came between Ibrahim and Muhammad but that called their people to be upright/hanif in their submission to God 10:72,84,98:5.
In pre-Islamic times, the term hanif had a strict monotheistic connotation. It was used in contrast to those that abhorred polytheism, but also who rejected the God incarnate of the Christians on one side and the ethno-centered monolatry of Judaism. It applied to those who exerted themselves to return to their original predisposition to uprightness as exemplified by Ibrahim. Like him, the prophets that followed him were all voluntary self-submitters, meaning Muslims, steadfastly constant on the path of servitude to God until their last breath 2:132-3,5:44,12:101,27:44 (the Queen of Sheba voluntarily submits). All belonged to the same community, under the same purpose 3:44,21:92,23:52-3, preaching monotheism 42:13.
They are not responsible for the perversion of their message by their followers, including potentially the followers of the last prophet
42:14,21:93,23:53"But they cut off their religion among themselves into sects, each part rejoicing in that which is with them".
These prophets all followed the same pattern of spiritual thought, hence the necessity for anyone to reject any proposition that clearly goes against the re-establishment of that way 3:83-5. No appellation therefore is of any importance in Islam, so long as those claiming to belong to a certain group, submit themselves in words and deeds to the divine will as expounded by a prophet of their time 2:62,5:69. These 2 verses, which speak of righteous believers of the past as is clear from the context, are Medinan. They were recited in Medina after the prophet was confronted to the rejection of some among the people of the book. The idea often propounded by orientalists as regards Islam's supposed initial conciliatory tone towards other faiths, which then changed after the prophet's conflicts with Jews and Christians is therefore baseless. Further, Sura 5 is universally recognized as among the last revealed, much later than sura 3. The contemporaries of the prophet among the people of the book are spoken of in both Medinan and Meccan suras 2:121,3:113-115,199,4:162,7:159-170,17:107-9,28:52-4 where they are either praised or condemned, irrelevant of the political tensions with Muslims, as is here the case for Christians in a late Medinan revelation
5:83"And when they hear what has been revealed to the Messenger, you see their eyes overflowing with tears because of what they have recognized of the truth. They say, "Our Lord, we have believed, so register us among the witnesses".
The appellations of Jewry or Christianity came into being after the time of the Patriarchs, and long after the times of Moses or Jesus 2:140. Objectively, these terms do not carry any connotation in relation to the divine will, as opposed to self-submission to God, as is intended with the descriptions of "Muslim" or "Islam". They are rather labels describing an affiliation to a race or individual.
The very early few ones that believed in Jesus, and their contemporaries that followed in their footsteps werent even known as Christians at first but as Nazarenes. They were strict followers of the Torah and its laws, as Jesus enjoined on his community. These 120 small band of believers in Jesus, an inconsequential number considering the spectacular wonders that accompanied his life, death and resurrection, were the followers of "the way" Acts19:9,23,22:4,24:14,22 and known as the Nazarenes Acts24:11. The Quran calls them nasara from nusra/help in reference to those few core elements that valiantly stood by him, when he started sensing disbelief among his followers 3:52,61:14. This inner circle are not the cowards presented in the NT as fleeing Jesus when adversity came or unable to understand most if any, of his teachings which is why they abandoned his instructions to abide by the law soon after his death. In the Quran they pray Allah to make them witnesses of the truth, that their life becomes an embodiment, a testimony to Jesus' teachings.
"Christian" is a later appellation Acts11:26. In fact the word Christian itself is in reference to the belief that those who hold that qualification are anointed with God's oil, according to the earliest Christians such as Theophilus.
Nasara is phonetically close to the historical Nazarene/Nazoraios (Greek) or Nasraya (Syriac) Acts24. In the region of the Levant from where the Christians of the Hijaz originated, Christians called themselves Kristyane. It is expected that the Quran would address them by that same name just as it addresses Jews and other groups by their own names. Instead it chose to bring back to the spotlight an appellation forgotten by Christians themselves, found in their books, in reference to the first followers of Jesus, so as to illustrate how far they have gone astray. The last revelation this way vindicates Jesus' true followers, the Nazarenes, by bringing them back to the forefront of history after they had been relegated to darkness by the Christian pauline movement.
Another similarly remarkable feature of the Quran, is in its emphatic description of Jesus' mission as exclusively meant for the Israelites. To the Jews of 7th century Arabia, as is the case today, the reason for Jesus' mission and to whom it was directed to, was of no importance. No Jew would have walked around teaching the notion that Jesus was sent to the Jewish tribes. Christians on the other hand, teach that Jesus' mission was meant for all of humanity. The NT itself makes the claim, contradicting itself. It is thus expected for a 7th century Arab who is neither a Jew nor Christian, and who awkwardly decides to reveal Jesus' target audience, to similarly state that Jesus was sent to all people. Or at the very least that he was sent to Christians just as Moses was sent to the Jews.
Then the Quran addresses the Israelites as those who literally 62:6"became Jews" because what Moses and the other Israelite prophets really taught was essentially Islam, or lit. volontary self-submission (to the divine will). There is a reason why the Quran exposes it as utter ignorance to claim that the patriarchs and the tribes/asbat were Jews; the Torah itself makes no mention of those people as Jews, rather as Israelites.
The root of "hadoo" includes the meaning of "those that were guided" and the Quran has attached this meaning to the Jews obviously because no other people ever received such manifest, continuous guidance. There are no Jewish prophets prior to Moses and there are no Christian prophets at all and all true prophets are Muslims in principle. So the most that can be said in this regard is that among those prophets whom the prophet Muhammad emulated, are some Jewish prophets.
Further reading answering Sam Shamoun "QURAN ONLY DILEMMA: HOW MANY PATHS TO PARADISE?"