According to the Quran a Muslim is one who has absolutely surrendered to Allah and his commands and believes in pure Tawhid (the oneness of God) that isn’t tainted with any Shirk and this is why the Almighty has introduced Prophet Abraham as a true Muslim in the Quran.
According to the Quran the true religion is Islam (surrender) (ان الدین عندالله الاسلام) and therefore all who have accepted religions of their time and have obeyed it’s commands are considered Muslims.
All of those who embraced the holy religion of their time are called Muslims by the Quran, meaning that Jews and Christians were Muslims until they had to change to the new religion which was Islam, because they had surrendered to Allah and if they were named Christians and Jews it was only because their prophets were different not that they had not surrendered to Allah.
It is obvious that today the term Muslim is used only for those who embrace the religion of Prophet Mohammad, because they have shown their surrender to Allah through believing in Islam and obeying his commands. According to this definition today people of other religions are not considered Muslims because they have actually rejected surrendering to Allah through turning away from the new religion (Islam) that was sent down for them and they are no longer considered Muslims.
It must be noted that a true Muslim is one who not only believes in Islam but actually practices it in his life. So not only should Muslims submit to the one God and believe in the prophets but they should also act according to Islam’s social teachings like respecting other people’s rights in society and it’s teachings that relate to one’s personal life like fasting and praying. In the Quran a true Muslim is (usually) referred to by the term “Mu’min”.