Muslim (In Arabic مُسْلِمًا from the Arab-Persian Muslimān) is the name of a believer that professes Islam. Both terms comes from the Arabic word “one who submits [to GOD, to the Faith]”.

Islam is name given to the Abrahamic religion that follows Mohammed as prophet. In Arabic literally means “submission” (to the will of GOD), from root of aslama “he surrendered, he submitted, he resigned” causative conjunction of salima “he was safe,” and related to salam “peace. 
In late 1800 Islam become the official denomination of the religion, name that is not related to a person or ethnic group, like in the majority of religious movement, but to the central idea of the religion.

To be consider a Muslim it is necessary only to utter with true faith the Shahada, a declaration of faith that professes that there is only one GOD and that Muhammad is GOD’s messenger.^{[note a]} It is a set statement normally recited in Arabic: “lā ʾilāha ʾillā-llāhu muḥammadun rasūlu-llāh” (لَا إِلٰهَ إِلَّا الله مُحَمَّدٌ رَسُولُ الله) “There is no god but GOD, (and) Muhammad is the messenger of GOD.”^{[note b]}

The analysis below refers to the 67th verse of chapter 3 (sūrat āl ʿim’rān):

“Abraham was neither a Jew nor a Christian, but he was one inclining toward truth, a Muslim [submitting to GOD]. And he was not of the polytheists.”
(Qur’an 3, 67)

Conclusion

Despite what is often affirmed in the Islamic sphere, Islam, like many other religions, is born in a free environment and without a denomination. Only during the following centuries the term was coined to indicate the believers of this religion. The Prophet Mohammed (PBUH) did not want to create a new movement, but only wanted to restore a true worship: “To love the One GOD through voluntary submission”. The aim was also to prevent believers, as happened in Christianity, from forgetting the true foundation of the doctrine during the generations in the following centuries and bind themselves to an earthly tradition, composed purely of human laws.
If one studies the Qur’an in this perspective, and does not give to the term Islam or muslim the meaning of “religious system” and “believer of a certain doctrine”, it will discovers an ideology based exclusively on pure faith in GOD. The LORD of Abraham, Isaac, Jacob, and all the prophets of the Old Christian Testament, a new way to believe that recognizes both the prophecy of Jesus (but not his Divinity in terms of “the same substance as the FATHER”) and the new revelation specific to the Arabic-speaking people who until then have been only servants of the two dominant growing monotheistic faiths (Judaism and Christianity).

Note

^{[note a]} The Pillars of Islam in Oxford Islamic Studies Online Archived 26 April 2017 at Wikiwix

^{[note b]} Gordon, Matthew; Gordon, Professor of Middle East Islamic History Matthew S (2009). Matthew S. Gordon and Martin Palmer, ”Islam”, Info base Publishing, 2009. p. 87. ISBN 9781438117782. Retrieved 26 August 2012.