The Muslim
Claims of belief, faith and conviction are not enough, and must be reflected in complete submission to the religion of Allah which is what makes a person a Muslim. A Momin can yield to temptation and become a kafir which is the opposite of Muslim. The prayer is therefore always to die as a Muslim because that is the ultimate goal of a Momin.
(7:126) …Our Lord! pour out on us patience and constancy, and take us in death unto you as Muslims!
(15:2) Again and again will the kafaru wish that they had been Muslim.
(16:89) One day We shall raise from all Peoples a witness against them, from amongst themselves: and We shall bring thee as a witness against these (thy people): and We have sent down to thee the Book explaining all things, a Guide, a Mercy, and Glad Tidings to Muslims.
(16:102) Say, the Holy Spirit has brought the revelation from thy Lord in Truth, in order to strengthen those who believe, and as a Guide and Glad Tidings to Muslims.
(27:38) He said (Solomon to his own men): "Ye chiefs! which of you can bring me her throne before they come to me as Muslim (in submission)?"
(28:53) And when it is recited to them(the devout Christians), they say: "We believe therein, for it is the Truth from our Lord: indeed we have been Muslims from before this.
(41:33) Who is better in speech than one who calls (men) to Allah, works righteousness, and says, "I am of those who are Muslim "?
(43:69) (Being) those who have believed (amanu) in Our Signs and been Muslim.
(46:15) …."O my Lord! Grant me that I may be grateful for Thy favour which Thou has bestowed upon me, and upon both my parents, and that I may work righteousness such as Thou mayest approve; and be gracious to me in my issue. Truly have I turned to Thee and truly I am Muslim."
(51:36) But We found not there any just Muslim persons except in one house(house of prophet Lut):
(68:35) Shall We then treat the Muslimeen like the Mujrimin (People of Sin)?
One Who Is Not A Muslim Is Not A True Momin
(24:47) They say, "We believe and have faith (aamanna) in Allah and in the messenger, and we obey (wa atana)": but even after that, some of them turn away: they are not (really) Momineen.
(29:11) And Allah most certainly knows those who believe (aamanu), and as certainly those who are Hypocrites.
A true Momin is also a Muslim. A Momin may or may not be a perfect Muslim, if swayed by temptation, arrogance or selfishness to transgress the limits prescribed by Allah, which is why the verses address the believers and warn them against becoming kafir by their behaviour
Who are the Momineen and the Muslimeen? | Naseer Ahmed, New Age Islam